The two parties took a decision following discussions with Chief Minister Prithviraj Chavan at a meeting here Wednesday.
"Chief Minister Prithviraj Chavan today spoke to Shiv Sena executive president Uddhav Thackeray and requested that it would be appropriate if the election was held unopposed," Shiv Sena leader Subhash Desai told mediapersons.
He said that since the election was being held to fill the vacancy left by the untimely demise of former union minister and two-time state chief minister Vilasrao Deshmukh, the opposition has decided not to put up an opposing candidate.
Leader of Opposition in the state assembly Eknath Khadse said after consultations with Chavan and since a woman candidate has been nominated to further the cause of the backward Marathwada region, the opposition would not challenge her in the Rajya Sabha election.
Patil's name was approved by Congress president Sonia Gandhi Tuesday for the Jan 12 Rajya Sabha by-election, necessitated by Vilasrao Deshmukh's death, whose tenure was to end April 2, 2018.
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Patil, 54, had briefly left the Congress to join the BJP in 1996 and was elected as its nominee to the 11th Lok Sabha. But she returned to the Congress in 1998.
Considered close to former union minister and present Punjab Governor Shivraj Patil, Rajni Patil's nomination threw off attempts by Chavan and state Congress chief Manikrao Thakre to get a ticket for their own candidates.
Other hopefuls like Mushtaque Antulay, Muzaffar Hussein, Rashid Alvi and even actress Naghma were considered strong contenders for the seat.