On Wednesday night, 25,000 people had been evacuated from their homes but the number doubled as water levels continued rising, they said.
"The Ukai dam is still above the danger mark," Narotam Patel, water resources minister of Gujarat state told reporters.
Water released from the dam as a precautionary measure had caused extensive flooding in the city.
But rains had stopped and if dry weather continued the floods could recede, Patel added.
Surat, a centre for textile manufacturers and diamond polishers, has a population of about 2.5 million people.
United News of India said about 75,000 people have been moved in six flood-hit districts of south and central Gujarat. The news agency also said the state was seeking the army's help in rescue and relief operations.
Police in neighbouring Maharashtra state said heavy rains and flooding were also reported in the towns of Nashik and Jalgaon.
- Reuters - Thomson Reuters Foundation
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