Fourteen headstones were badly damaged in the graveyard beside the Anglican Church of St John the Baptist in Reid on Monday night.
The damage is estimated to be about $20,000.
St John's is the city's oldest church, consecrated in 1845, 70 years before Canberra was named the national capital.
The churchyard cemetery contains headstones dating from 1844.
Police are investigating and urge anyone with information to contact Crime Stoppers.