Surrey's Ansari, 23, hurt his bowling hand against Lancashire on day two of their County Championship match, hours after receiving a first Test call-up.
He was taken to hospital and Surrey later confirmed the injury was an "open dislocation", adding that it would be assessed in the coming days.
England begin their three-Test series with Pakistan in the UAE on 13 October.
They leave in a fortnight's time, arriving in the UAE on 30 September and playing two warm-up games in Sharjah.
Before then, Surrey face Gloucestershire in the One-Day Cup final at Lord's on Saturday.
"It didn't look very good. He was in a lot of pain in the dressing room," said Surrey director of cricket Alec Stewart.
"What should have been a day of celebration for Zafar, we are now hoping he will be OK. The way he was, there must be some doubt.
"He dropped a catch stood at cover point. The ball came out of the sun, he saw it late and it hit him hard on the left thumb. He is not in the greatest shape."
Left-arm spinner Ansari, who has taken 44 wickets and scored more than 700 runs this season was picked to provide England with a third spin option after Moeen Ali and Adil Rashid.
As well as Ansari, Nottinghamshire batsmen Alex Hales and James Taylor were also called up, but Yorkshire pair Gary Ballance and Adam Lyth both missed out.
All-rounder Zafar Ansari's hopes of an England Test debut are in doubt after he dislocated his thumb while fielding.