Defender Christopher Jullien tested positive for COVID-19 after the team returned to Scotland ahead of Monday's Premiership clash with Hibernian.
Although all other squad and staff members returned negative tests, Lennon, assistant John Kennedy and 13 first-team players are self-isolating after being deemed close contacts.
The reigning champions remain insistent they followed "rigorous" COVID-secure protocols and that the threat of contracting the virus would have been similarly high had they stayed in Scotland.
In a statement, Celtic said: "Clearly we are hugely disappointed, as we know our supporters will be. The contacts were identified during the period from Wednesday last week, primarily around flight and team coach travel, during which time Celtic applied the same rigorous protocols used for pre-season training camps, UEFA match travel and for all domestic match arrangements in Scotland.
"These protocols have served us well in the past, as the club has not had one positive case in our own 'bubble' until now. As we have already stated, Celtic's decision to travel to Dubai for a training camp was for performance reasons. Whilst we were in Dubai, the announcements made on January 4 significantly changed the COVID landscape.
"The reality is that a case could well have occurred had the team remained in Scotland, as other cases have done in Scottish football and across UK sport in the past week.
"Celtic has done everything it can to ensure we have in place the very best procedures and protocols. From the outset of the pandemic, Celtic has worked closely with the Scottish Government and Scottish football and we will continue to do so."
The Scottish Premiership has been suspended until further notice following the outbreak, with Celtic holding a 13-point lead over arch rivals Rangers at the summit.
Lennon admits some of his players might be struggling during the enforced absence from football and says the club are keeping a watchful eye on their mental health.
"They're like caged animals," he told BBC Sport. "These are young, fit men who're used to an almost regimented way of living. Their routine is training and playing. All of that is gone. Some of them will be cooking for themselves for the first time in their lives.
"Mentally, the change can put a strain on them. They're used to intensity and suddenly it's not there. We're very aware of the mental [health] side of this. We all need to keep our wellbeing in order.
"As long as I can get out and get some exercise for my own peace of mind then I'm fine. The silence is deafening when you go out for a walk. The place is deserted. We just have to ride it out as best we can. We're all in the same boat."
While understandably missing football, Lennon believes the break could be used as an opportunity for the game to find better ways of connecting with local communities when it returns.
"I'm really missing football," he added. "I'm missing the players, the staff, the games, the colour, the noise, but it's no bad thing to take a moment and appreciate what you've got.
"I think football will mean a lot more to a lot of people when it returns. What I'm seeing now is us going back to our roots, going back to community life with people looking out for each other and maybe we'd gone away from that.
"What's happening is tragic but everybody is pulling together to try to get through it and that's brilliant."
The Hoops equalled the record for the most title wins in a row after the Premiership season was brought to an end by the Scottish Professional Football League following consultation with the 12 top-flight clubs.
The final standings were calculated on a points-per-game basis, with Celtic having been 13 points clear of Glasgow rivals Rangers when fixtures were halted in March due to the coronavirus pandemic.
Lennon, who was also in charge for the first three championship wins and returned to the club in February last year, declared this success the pick of the bunch.
"To be sitting here now as the manager of the nine in a row, and having played a huge part in that, fills me with so much pride," he told Celtic TV.
"It feels wonderful and I'm so proud of the players. It's an incredible record and to be part of that is something very special, and I think it's thoroughly deserved as well.
"It's the best, no question it's the best and I've enjoyed the season immensely. I enjoyed the European campaign and winning the League Cup and I enjoyed working with the players every day, I enjoyed working with my staff.
"Whether you look at the first half of the season or the second half of the season, we've played some brilliant football throughout, and then you throw in the European campaign, you throw in the League Cup. A lot of that gets overlooked with all that's been going on around Scottish football of late.
"The style of play pleased me, the amount of goals pleased me, and we had massive contributions from numerous individual players as well."
