The Croatian opened the scoring but then limped out of the action after 32 minutes after injuring himself when making a challenge on Albion defender Gonzalo Jara.
Modric left the ground on crutches and is to undergo a scan after suffering a blow on the same bone which was broken last season and sidelined him for several months.
Spurs boss Harry Redknapp is already resigned to being without Jermain Defoe and Michael Dawson for lengthy spells after being injured on England duty. It was not the news Redknapp was hoping for before Tuesday's Champions League clash away to Werder Bremen.
Redknapp said: "He is going for a scan but he broke the bone in his leg last year against Birmingham and he got a kick on the same spot today. He is in a lot of pain today. It doesn't look great.
"We will wait and see what the scan says but it certainly doesn't look very good. We don't know yet if the leg is broken again. If he has got another break, you are talking months again.
"I am just hoping it is good news for a change. Defoe has had the ankle operation and he is out for 12 weeks and Dawson is another one.''
Redknapp was pleased with Rafael van der Vaart's debut following his £8 million move from Real Madrid.
He said: "In the first half we had so much possession and looked very comfortable. The goal just before half-time brought them back into the game. Credit to them, they got stronger as the game went on. I thought we tired.
"Van der Vaart ran out of steam. I thought he was different class in the first half. Modric and Van der Vaart playing together is going to be clever and you'd think Defoe would feed off them in the long term.''
He said: "At this moment, we are disappointed not to have won the game given the chances we created in the second half. But after a good night's sleep, we will wake up and take the point because Spurs are a fantastic team. We need to take courage from the last performances and try and build on them.''