The news emerged just hours before the Lionesses face Northern Ireland at Southampton's St Mary's Stadium in their final Group A game.
Dutch boss Wiegman will isolate at England's team hotel.
In a statement, the Football Association said: "England head coach Sarina Wiegman has tested positive for COVID and will undertake a period of recovery at the squad’s base camp. Assistant coach Arjan Veurink will lead the team for tonight's fixture against Northern Ireland.
"Wiegman will remain in remote contact with the players and technical staff and will be monitored regularly with a view to returning to all elements of her role as soon as possible."
England have already won their group so know their quarter-final will take place next Wednesday against the Group B runners-up, who will be Denmark or Spain.
A number of COVID-19 cases have already hit the tournament, with Netherlands striker Vivianne Miedema a notable recent case.
Miedema scored twice for the Netherlands in the Euro 2017 final win over Denmark, when Wiegman was the Dutch team's head coach.
The 52-year-old Wiegman took up her appointment as England boss in September 2021, handed the task of leading the hosts into the European finals.
Wiegman appeared at an England pre-match news conference alongside goalkeeper Mary Earps on Thursday, and took training. England started their campaign by winning 1-0 against Austria before inflicting an 8-0 thrashing on Norway.
Lionesses boss Sarina Wiegman missed her side's final group game after testing positive for COVID-19, but the hosts made another statement at St Mary's Stadium on Friday.
First-half goals from Fran Kirby and Beth Mead set England on their way, as they became the first team ever to score over 10 or more goals in the group stage of the women's Euros without conceding.
Alessia Russo scored England's third just minutes after coming on at half-time with an excellent header and helped herself to a brace in the 53rd minute, when an exquisite turn on the edge of the box made the space for her to lash home and make it 4-0.
Kelsie Burrows summed up a miserable night for Northern Ireland when she scooped into the back of her own net.
Group A winners will face the runners-up in Group B on Wednesday for a place in the semi-finals.
Norway headed into their last group game knowing that only a win would see them through, due to their inferior goal difference after they were thumped 8-0 by England.
Austria only needed a draw, and they went ahead after 37 minutes when a superb header from Nicola Billa nestled into the bottom corner.
Martin Sjogren's side were unable to respond, so Austria will face Germany in the last eight at the Brentford Community Stadium on Thursday and Norway are heading home.
The two-time champions launched their quest for a third European title in a commanding manner, with Julie Blakstad, Frida Maanum, Caroline Graham Hansen and Guro Reiten all getting on the scoresheet.
Norway failed to find the net in three matches at Euro 2017 but took just 10 minutes to open their account this time around; Reiten releasing Blakstad to drill past Jacqueline Burns at her near post.
Their lead was doubled just three minutes later. Maanum dispossessed Chloe McCarron high up the field, before receiving Ada Hegerberg's return pass and slotting into the empty net.
Hansen made it three from the penalty spot in the 31st minute after Nadene Caldwell was penalised for handball.
The lowest-ranked team in the competition, Kenny Shiels' side produced a spirited response after the break and pulled a goal back within four minutes of the restart when Julie Nelson headed in from close range.
But Martin Sjogren's team had the final word and thwarted any potential comeback five minutes later when Reiten beat Burns with a delicious 20-yard free-kick.
White was twice on target as England hammered Norway 8-0 as Wiegman's side recorded the biggest win in men's or women's European Championship history.
England also became the first team in any Euros to net eight goals as they sealed top spot and a place in the knockout stages.
While it was a successful outing in Brighton on a team level, White also moved just one strike behind Rooney's record 53 goals for England.
White was quick to insist that Rooney's benchmark is not her priority after the game, before online trolls posted unnecessary questions surrounding the validity of her record in the women's game.
Wiegman jumped to the defence of her star striker on Thursday as she spoke ahead of the group-stage clash with Northern Ireland, insisting talented ability is the same in the men's and women's game.
"I just talk to my squad and to Ellen. Everyone can have their opinion, but I think what she's done is amazing, really good," Wiegman told reporters.
"The player and person she is in our team – such an important role. What she has accomplished on the pitch and also off the pitch is really, really great, and she's so valuable for this team. So maybe I would say that to those people.
"It doesn't matter if you're a man or a woman – if you're great, you're great.
"For her to have achieved that, and the success she's had over such a long time, that tells you everything you need to know.
"She's been fantastic for England for a very long time, so of course it's great to have her on my team."
White will hope to at least equal Rooney's record against Northern Ireland, who have lost all eight of their previous meetings with the Lionesses, scoring just two goals to England's 44 in the process.
