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.

Dayow Mohamed Hassan, 44, was buried neck-deep and pelted to death with stones by al-Shabab fighters.
He was convicted of being in an adulterous relationship with a woman and impregnating her, despite having two wives, an official said.
Al-Shabab occasionally passes such sentences for sexual offences in areas it controls in Somalia.
In 2014, a teenage boy was stoned to death after being convicted of raping a woman.
In 2008, a young girl was killed in a similar manner after being convicted of adultery.
In the latest case, a  woman filed a complaint of rape against Hassan, but the court tried him for adultery as it is easier to prove, says BBC Somali's Mohamed Mohamed.
Hundreds of people watched him being stoned death in Ramo Adey village in the south-central Bay region, said Moalim Geedow, the al-Shabab governor for the area.
"The man had a third woman who was a divorcee... He deceived her, saying that he went to a sheikh [religious leader] and that he married her," Mr Geedow told Reuters news agency.
"However, when the woman got pregnant, the two families debated and there was no trace of valid matrimony. The court ruled he did not marry her legally and he was stoned to death."
Al-Shabab is fighting to overthrow the weak UN-backed government in Somalia and impose its own strict interpretation of Islamic law.
It has lost control of many towns and cities to a 22,000-strong African Union force supporting the government.
But the group, linked to al-Qaeda, still has a strong presence in many rural areas.
All-rounder Zafar Ansari's hopes of an England Test debut are in doubt after he dislocated his thumb while fielding.
[NEXT_CONCEPT]
Somali militants have stoned a man to death after an Islamic court convicted him of adultery.