The New Zealand batting mainstay sustained the injury during the season opener against Chennai Super Kings here last Friday.
Williamson sustained the injury to his right knee while attempting a catch during the opening match at the Narendra Modi Stadium.
"It is sad to lose Kane to injury so early in the tournament. We wish him a speedy recovery, with the hope of seeing him in action very soon," said GT's director of cricket, Vikram Solanki, in a press release.
Williamson will now head home to New Zealand for further assessment, the defending champions said in the press release.
Gujarat Titans will finalise a replacement for the right-handed batter and an announcement will be made in due course.
The 32-year-old got injured following a nasty fall while fielding on the boundary during the CSK innings. He had limped off the field in the 13th over.
Williamson, who was making his Gujarat Titans debut, intercepted a ball headed for a possible six off CSK opener Ruturaj Gaikwad's bat.
He managed to palm the ball into the field of play before it bounced onto the boundary ropes. But he fell awkwardly on the ground and clutched his right knee in pain.
He was taken off after receiving on-field treatment and did not come back to bat with B. Sai Sudharsan coming on as a substitute fielder first and later he took Williamson's place in the Titans' playing XI under the Impact Player rule.
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Kolkata (PTI): Chief Minister Mamata Banerjee cut short her speech at a rally in her Bhabanipur constituency, alleging that the BJP was deliberately playing loud music from a nearby public meeting.
A peeved Banerjee said despite having the required permission of the Election Commission, her rally in Chakraberia was disrupted by the BJP, "who want to capture Bengal by intimidation and threat".
"It is not possible for me to go ahead with this meeting. If they can do such a thing in my constituency, imagine how undemocratic the BJP is. If they behave like this, I have to take legal action," she said.
"This is an insult, humiliation. BJP is stepping on our toes to instigate trouble. Not possible to address the gathering in this situation. I am leaving the stage. Please vote for me in your protest," she added.
Banerjee was then seen calling someone over and venting her grievances.
Before leaving the stage, she said, "I will hold a rally tomorrow at the same spot."
TMC supporters then rushed towards the BJP rally, which was later addressed by Leader of the Opposition Suvendu Adhikari, but security personnel intervened and prevented the situation from escalating.
TMC workers later staged a demonstration outside the local police station and filed a complaint, alleging that the BJP violated the model code of conduct.
A senior TMC leader said another complaint will also be lodged with the Election Commission.
Asked about Banerjee's allegations, Adhikari told reporters after the rally he held nearby, "Her reaction shows she is nervous about the imminent loss."
"There was no violence, no obstruction in her meeting and her behaviour shows her nervousness. On May 4, people of Bhabanipur will celebrate the victory of the BJP," he claimed, alleging that the TMC also tried to disrupt his meeting by playing loud music.
South Kolkata's Bhabanipur, one of the battleground seats in the West Bengal elections, will vote in the second phase on April 29.
