Reyna, 17, was named in Dortmund's line-up as the Bundesliga returned from a two-month suspension due to the coronavirus pandemic but sustained an injury in the warm-up. He was replaced by Thorgan Hazard.
Hazard teed up the opener for Erling Haaland and scored one himself in between a double for Raphael Guerreiro, helping BVB cruise to three points at an empty Signal Iduna Park.
Schalke lost Jean-Clair Todibo to a muscular injury at half-time, while Hazard hobbled off when he was replaced by Jadon Sancho in the 79th minute.
Favre insisted the Belgium international was only struggling with cramp, but he expects a number of players will suffer from niggles as the Bundesliga gets back up and running.
"A lot of teams will have a few players who will be injured," said Favre. "We started very late with the 10 against 10 games, tackling and so on.
"I hope Reyna has nothing. It won't be long for [Axel] Witsel and [Emre] Can, [Dan-Axel] Zagadou won't play again this season.
"Marco Reus has not yet played with the team. Nico Schulz has injured himself again, he is not allowed to do anything for two to three weeks.
"Hazard only had cramp, no injury."
Dortmund players kept their distance when celebrating – a touch of elbows the most contact they made with one another – while substitutes were spaced out on the sideline and wore masks.
Favre acknowledged the atmosphere behind closed doors was unusual but was proud of the way his team performed.
He said: "4-0 against Schalke - that's quite okay. The key was that the team played well together, also defensively. That was very, very special.
"There wasn't any noise, you shoot at the goal, make a top pass, a goal - and nothing happens. That's very, very strange. We really miss our fans.
"It was a completely different game than usual. It's hard to judge how good the game was. I had the feeling that it wasn't as committed as planned. The players were very focused on their task."
An error from goalkeeper Markus Schubert preceded Guerreiro's opener, while Dortmund's last two goals came at the end of swift counter-attacks.
Schalke boss David Wagner said: "We didn't have a good game, and at really bad moments we conceded the goals. At least two goals would have been easy to defend.
"Derby defeats are unpleasant in principle, even in this bizarre atmosphere. The feeling of the second half of the season is not there yet. The situation is quite extraordinary.
"I don't think we had any major physical deficits. We had deficits in defending the right spaces."
Sancho was the subject of intense transfer rumours in the close-season as Manchester United reportedly attempted to prise the England international away.
Dortmund maintained early on that Sancho was not for sale once an August deadline passed, and they successfully resisted United's apparent attempts to make a deal happen.
But, while no move transpired, Favre suggests it was not a case of no harm being done.
Sancho has only had a hand in two goals (two assists) in four Bundesliga matches at the start of 2020-21, a somewhat disappointing figure by his usual standards.
Favre believes the pre-season saga could have affected him.
"Every player has slow periods," he said ahead of Wednesday's Champions League clash with Zenit.
"There was a lot of talk about Jadon in the summer, something like that can also have an impact.
"But no player is consistently in top form for an entire year, that's impossible. You have to accept that."
Last season, Sancho created a total of 69 goal-scoring chances in the Bundesliga, ultimately leading to 16 assists. He also scored 17 times, meaning he was involved in 33 goals in 32 games.
While his key pass frequency was 2.71 per 90 minutes in 2019-20, that has only decreased slightly to 2.04 this term, therefore he is still creating opportunities.
Nevertheless, Sancho is already behind in regards to his overall productivity in comparison to the previous season.
Favre returned to the Ligue 1 club for a second stint in charge in June 2022 as they invested ahead of the new season.
The former Borussia Dortmund boss had guided Nice to Champions League qualification in 2016-17, but his latest spell did not yield the same success.
Despite making a series of high-profile signings, including Aaron Ramsey, Ross Barkley and Kasper Schmeichel, Nice are down in 11th in Ligue 1.
The final straw for Favre was Saturday's cup elimination at the hands of lower-league opposition, with Nice winless since the World Cup break.
Didier Digard will take charge of Nice "until further notice", with a Ligue 1 double-header against Montpellier and Reims this week.
A Nice statement added of Favre: "As the two parties now go their separate ways, everyone at the club would like to show him the utmost respect, as he will remain a special member of the Rouge et Noir family, with the 2016-17 season having left an indelible mark in the hearts of Le Gym fans everywhere."
Favre became the second Ligue 1 coach to be removed from his post on Monday, following Julien Stephan's dismissal at Strasbourg.
Stunned by lowly Mainz in midweek, Lucien Favre's side responded to the shock home defeat by ending Leipzig's 13-match unbeaten league run, keeping Timo Werner particularly quiet in his final home game before joining Chelsea.
