The 25-year-old Ivorian appeared to get his foot stuck in the turf at Hongkou Stadium in Shanghai and a concerned Solskjaer said the player had twisted his knee.
Solskjaer, who had been linked with a move for Leicester City central defender Harry Maguire even before losing Bailly, said: "It's never nice when you get an injury.
"It's not worth it when you lose one. He's done his knee but we are not sure how bad it is.
"We need to get back to Manchester and do the scan.
"Let's hope for the best."
Bailly, who had only come on as a substitute for Chris Smalling at half time, was replaced in the 56th minute.
It took the gloss off a satisfactory evening for United, who have now won all four pre-season friendlies.
Teenager Angel Gomes squeezed in the winner 10 minutes from time in what was an occasionally bad-tempered friendly against their Premier League top-four rivals.
French striker Anthony Martial put United ahead in the first half, before Spurs substitute Lucas Moura replied with a scrappy effort in the second.
After wholesale changes from both sides -- Solskjaer swapped out all 11 starters at the break -- Spurs had looked the more dangerous, before the 18-year-old Londoner Gomes struck.
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The Norwegian Solskjaer, under pressure to prove that he is the man to take United back into the Champions League, named a strong side that included wantaway midfielder Paul Pogba and new signings Daniel James and Aaron Wan-Bissaka.
Counterpart Mauricio Pochettino fielded a more experimental team, but started the England international duo of Dele Alli and Harry Kane, along with new man Tanguy Ndombele.
United nearly took the lead on just four minutes when Martial fired across stand-in goalkeeper Paulo Gazzaniga, but his powerful effort struck the post.
Despite the fierce humidity there was an edge to the International Champions Cup game not always present in pre-season friendlies.
Attacking midfielder Alli, perhaps frustrated after missing a golden chance, was booked on 12 minutes after a second late challenge in front of a full house. He was booed off when subbed on an hour.
Martial, whose United career has threatened to peter out at times, made no mistake on 21 minutes when he rifled the ball under Gazzaniga from close range.
United were incensed when Moussa Sissoko left the sprightly winger James in a heap by the corner flag, suspecting a stamp by the Spurs midfielder.
Tottenham captain Kane angrily waded in and there was a scuffle, with Gazzaniga leaving his goal to join in and several United players also involved.
Andreas Pereira, a combative midfield presence for United, was next to be booked after he cut down Kane. Young Spurs defender Japhet Tanganga was yellow-carded too.
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United face Norwegian side Kristiansund in their next friendly, on Tuesday, while Spurs play Real Madrid next.
Solskjaer would not be drawn on whether he now intends to step up his pursuit of Maguire, the England defender who is also said to be of interest to Manchester City.
"We've had six centre-backs rotating here and all done well," he said.
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