The plaque, which has been missing for around two weeks, commemorates the bridge being built in 1791, bought for £130,000 in 1927 and declared free from tolls in 1932.
A plaque which marks the widening of the bridge in 1964 remains on the opposite parapet.
A spokesman for Lincolnshire County Council said it was unlikely the plaque had fallen off, and it was more likely it had been ‘removed from its mountings’.
The council is now looking to get a replacement.
The Trent Bridge underwent a face lift in December 2011 which included work to restore the plaques.