Goa Forward Party's Jayesh Salgaoncar and Vinod Palyekar, Congress' Philip Neri Rodrigues, Ravi Naik, Digambar Kamat and Tony Fernandes, and BJP's Pramod Sawant and Pravin Zantye were among the early voters.
The Goa Assembly has 40 members. However, 38 MLAs are eligible to vote in today's election as Vishwajit Rane (Congress) and Siddharth Kuncolienkar (BJP) have resigned.
Mr Parrikar, yet to be elected to the Assembly after he resigned as the Defence Minister and returned to the state, cast his vote in his capacity as Rajya Sabha member from Lucknow.
Three MPs from the state - Shantaram Naik (Rajya Sabha), Shripad Naik (Lok Sabha) and Narendra Sawaikar (Lok Sabha) will cast their votes in Delhi.
GFP, a BJP ally, is supporting the NDA candidate Ram Nath Kovind.
GFP leader and state minister Vinod Palyekar said his party had taken the right decision to support Mr Kovind. "We are part of the NDA. There is no question of voting for anyone else," he said.