Parrikar, the BJP candidate in the by-election, is pitted against the Congress' Girish Chodankar and the Goa Suraksha Manch (GSM) nominee, Anand Shirodkar.
The Sena, which is part of the BJP-led ruling coalitions in Maharashtra and at the Centre, is supporting the GSM in the bypoll.
Parrikar was not an MLA when he was appointed the Goa chief minister in March this year.
"When any chief minister contests an election, he should first resign from the post. When you fight as a chief minister, you do not provide a level-playing field to the other contestants," Sena leader Sanjay Raut told reporters here.
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Raut said the Panaji bypoll was being closely monitored in the political circles.
"The chief minister made several statements and announcements in the Assembly (during the Monsoon Session), keeping in mind the Panaji and Valpoi bypolls," he alleged.
The Rajya Sabha MP claimed that this amounted to "misusing power to influence the voters".
He said Parrikar should have stepped down as chief minister and waited for six months before getting elected and sworn-in to the post.
The Sena leader said his party had extended its support to the GSM's Shirodkar in the Panaji bypoll.
Talking to reporters, Shirodkar claimed the real fight in Panaji was between the Congress and the GSM, while Parrikar was "nowhere in the race".
"There is a strong undercurrent against Parrikar which he has sensed. He is already out of the competition. The real fight is between the Congress and the GSM," he said.