The Brazilian attacker, who opened the scoring before Jimmy Briand equalised in the second half, pulled up with apparent groin trouble and had to go off after 57 minutes.
Neymar walked straight down the tunnel to receive treatment after being replaced by Eric Maxim Choupo-Moting.
"I think it's the same injury, but I haven't seen yet," Tuchel told Canal+ after the match.
"We have to be careful, He said (before the game) it was not a problem playing today. Hopefully, we will have him back after the Strasbourg game."
"I was not 100 per cent," Neymar said after the game against Jurgen Klopp's team. "But it was an important match so, injured or not, I had to be there."
Neymar's goal against Bordeaux was his 30th strike in 32 league games since joining PSG from Barcelona in a world-record transfer last August.
PSG appeared to suffer a further blow in the 66th minute when Kylian Mbappe held the back of his right leg after putting PSG 2-1 ahead.
The France international initially suggested to the bench he needed to be substituted but was able to return to the game after undergoing treatment for cramp.
Bordeaux bounced back again, however, as substitute Andreas Cornelius equalised with six minutes left.
Next up for PSG is a visit to Strasbourg on Wednesday before a home match against Montpellier over the weekend.