Kapil Sharma said he was asked to pay a bribe of 500,000 rupees ($7,492; £5,632) to build his Mumbai office, despite paying huge taxes.
He tweeted, "Yeh hain aapke acche din? (Is this your idea of good days?)", referring to Mr Modi's campaign slogan in the run up to his 2014 poll victory.
The Mumbai civic authorities said the office structure was illegal.
But, they told reporters that they had begun an investigation into the corruption allegations.