The five judges are expected to announce their verdict in mid-November, according to Al Jazeera.
They heard 14 petitions challenging a 2010 lower court ruling that 1.12 hectares (2.77 acres) of disputed land be partitioned among Hindus and Muslims.
The destruction of the Babri Mosque in Ayodhya, a town in northern Uttar Pradesh state, in 1992 sparked massive Hindu violence against Muslims that left 2,000 people dead.
The judges started day-to-day proceedings in August after mediation proceedings failed to find a compromise between the two communities.