A local court in Delhi refused the brothers interim protection from arrest earlier on Thursday.
Their lawyer said at that hearing that Saurabh and Gaurav Luthra were on a business trip in Thailand, and said they were not the nightclub's owners but licensees.
The fire ripped through the Birch by Romeo Lane nightclub in Arpora around midnight on Saturday.
"We have detained them today in Thailand. We will bring them to Goa within a short span of time," Goa Chief Minister Pramod Sawant told reporters in state capital Panaji on Thursday.
Lawyer Tanvir Ahmed Mir said he did not have immediate confirmation of their detention but told Reuters on Thursday the brothers were facing a "vengeful government".
He said they had been in Thailand because they were in the process of setting up a restaurant in Phuket.
India has arrested six other people in the case so far, including five employees of the establishment.
The brothers' lawyer said in Thursday's hearing that staffers oversaw the nightclub's daily functioning and the Luthras could not be held culpable.
Indian authorities have offered compensation to the families of the victims, among them at least four tourists and 14 club staff.
Goa, a small coastal state, is a popular tourist destination especially among foreigners, offering beaches and hilly landscapes.
About 5.5 million tourists, including 271,000 from abroad, visited Goa in the first half of the year, according to government data.
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