Singh, arrested in the cash-for-votes scam, is on interim bail till Sep 19. He was put under medical observation Sep 13 after he complained of ill health.
Bachchan, who is in Delhi to attend the Bharatiya Gyanpith Award, was accompanied by his Delhi-based daughter, Shweta Nanda.
Amar Singh and two former Bharatiya Janata Party (BJP) MPs, Faggan Singh Kulaste and Mahavir Singh Bhagora, were arrested Sep 6 for their alleged involvement in an attempt to bribe MPs ahead of the July 2008 parliament trust vote.
Bachchan's visit follows Singh confidante and MP Jayaprada's jibe saying: 'The celebrities he helped, the famous people... Where are they?'