As per reports, the bail has been granted on furnishing a personal bond of Rs 15,000.
Earlier on Tuesday, Rane was sent to judicial custody after he was produced before the Magistrate Court in Mahad in the Raigad district of Maharashtra.
Rane was arrested in Ratnagiri district after FIRs were filed against him.
On Monday, he had accused Thackeray of ignorance about the year of India's independence at an event and said "I would have given a tight slap".
Shiv Sena leaders strongly condemned Rane's remarks. Party leader Vinayak Raut sought his removal from the union cabinet.
Due to his remarks, FIRs were registered against at several places including Nashik and Pune, based on the complaints filed by Shiv Sena leaders.
Pune City Police Commissioner Amitabh Gupta said a case has been registered under sections 153 and 505 of IPC at Chaturshringi police station and an investigation is being held.
Nashik Police said that remarks by Rane against the Chief Minister may aggravate the law and order situation. It instructed officials to follow all protocols necessary to arrest a Union Minister and Rajya Sabha member.
As per the protocol, the Vice president of India and Chairman of Rajya Sabha must be informed after the arrest of a Rajya Sabha member.
A verbal spat had erupted between supporters Rane and police at Sangameshwar Police Station in Ratnagiri.
Rane, a former Chief Minister of Maharashtra, was made Minister for Micro, Small and Medium Enterprises in the reshuffle and expansion of the council of ministers last month.