"The statement he has given is very shameful. It needs to be condemned," the Shiromani Akali Dal, or SAD leader told reporters in the parliament house complex in New Delhi.
The SAD is one of the oldest allies of the BJP.
She said the remarks show Mr Agrawal's mindset and hoped that Rajya Sabha Chairman M Venkaiah Naidu will take a call on it.
"When an elected representative speaks such language, it shows his mindset. It sends a wrong message to the young generation," she said.
Asked about action against Mr Agrawal, Ms Badal said: "He himself should feel ashamed. I have faith in Venkaiahji. He respects women a lot and will do the needful."
Foreign Minister Sushma Swaraj also conveyed her disapproval of the remarks in a tweet.
Shri Naresh Agarwal has joined Bhartiya Janata Party. He is welcome. However, his comments regarding Jaya Bachhan ji are improper and unacceptable.— Sushma Swaraj (@SushmaSwaraj) March 12, 2018
"Shri Naresh Agrawal has joined BJP. He is welcome. However, his comments regarding Jaya Bachchan ji are improper and unacceptable," she tweeted.
On Monday, Mr Agrawal said the Samajwadi Party had refused him a Rajya Sabha berth and gave it to a person just because she "could dance and act in the films".
"My stature has been equated with that of a mere film actress. Just because she could dance and act in films, my candidature (to Rajya Sabha) has been sacrificed for her. I haven't taken it kindly."
Mr Agrawal's term in the Rajya Sabha is ending next month and he had expected a re-election to the upper house. But his hopes were dashed when the party chose Jaya Bachchan to be its candidate.