India's 5% broken parboiled variety fell to $374-$379 per tonne, from last week's $386-$390.
The second wave has started affecting logistics from rice milling to transporting cargoes to the port, said Nitin Gupta, vice president for Olam India's rice business.
"Still, operations are not disrupted, but they could if cases continue to rise."
India's total COVID-19 cases passed 18 million on Thursday. The Indian rupee, meanwhile, remained weak.
Neighbouring Bangladesh also reeled from a new wave of infections that has forced the country into an extended lockdown until May 5, hampering rice harvesting due to a shortage of labour.
Traditionally the world's third-biggest rice producer, Bangladesh has emerged as a big importer after repeated floods last year damaged crops.
Meanwhile, Thailand's 5% broken rice prices rose to $470-$500 per tonne from $467-$500 a week ago.
"Prices went up slightly because there was some demand from Africa for parboiled rice," one Bangkok-based trader said.
Another trader said exporters have rice on hand to ship, but demand has not been spectacular. Demand from the Middle East has winded down during the month of Ramadan, he added.
Vietnam's 5% broken rice narrowed to $485-$490 per tonne on Thursday, the lowest since Dec. 10, from last week's $485-$495.
"Sales are slow as many traders are off for a long holiday weekend," a trader based in Ho Chi Minh City said. "Some exporters are still buying for the contracts signed earlier."
For the first four months of this year, Vietnam's rice shipments likely fell 10.8% from a year earlier to 1.89 million tonnes, but revenue likely rose 1.2% to $1.01 billion, according to the government's General Statistics Office.
(Reporting by Rajendra Jadhav in Mumbai, Khanh Vu in Hanoi, Patpicha Tanakasempipat in Bangkok and Ruma Paul in Dhaka; Editing by Arpan Varghese and Shailesh Kuber)
By Sumita Layek