New Delhi's foreign ministry last week said that it will closely monitor "any bearing on India's security and economic interests and takes all necessary measures to safeguard them".
In a written request, the Sri Lanka foreign ministry told the Chinese embassy in Colombo not to go ahead with the visit, an official involved in the process told AFP on Saturday.
"The ministry wishes to request that the arrival date of the vessel Yuan Wang 5 in Hambantota to be deferred until further consultations are made on this matter," the request says.
Sri Lankan President Ranil Wickremesinghe assured political party leaders on Friday that the controversial visit will not go ahead as planned.
Earlier this week, Colombo appeared to brush aside Indian concerns, saying the vessel was coming only to refuel and replenish supplies and would not undertake any work in Sri Lankan waters.
India objected strongly when two Chinese submarines berthed in Sri Lanka in 2014.
Former president Gotabaya Rajapaksa, whose brother Mahinda Rajapaksa borrowed heavily from China while president from 2005 to 2015, was forced to resign last month over Sri Lanka's worst-ever economic crisis, which is ongoing.