Caulker, 19, was injured following a collision with team-mate David James early in the FA Cup defeat on Saturday.
"Steven is going for a scan back at Tottenham to assess the damage," City boss Keith Millen told the club`s official website.
"We hope it is not too bad and we will keep our fingers crossed. We should know more in the next 24-48 hours."
Meanwhile, fellow defender Christian Ribeiro, who was also forced off during the third-round tie, will have to wait for a scan on his hamstring problem.
Millen added: "We have got to wait for the swelling to go down a bit so it will be a few days before we can really assess the damage."
Source: PA
Source: PA