Officers are looking for witnesses and dashcam footage following the fire on board the Wyre Lady in Sprotbrough Lock earlier this week.
On Wednesday, between 6pm and 6.30pm, it's believed the 82-year-old vessel that was used in WW2 was deliberately set alight.
The incident happened at Sprotbrough Locks where the Trans Pennine Trail runs along the canal.
Officers are keen to speak to any witnesses that were on the Trans Pennine Trail at Sprotbrough around the time of the incident that noticed anybody around the 'Wyre Lady', and any cars with dashcam footage from around the same time travelling along Mill Lane, Sprotbrough, over the River Don and the canal.
PC Josh Smith, investigating officer said: “The Wyre Lady boat is an impressive vessel with incredible history. She was built in 1938 as a railway passenger ferry. In 1939 the then named 'Ashton' was requisitioned by the Royal Navy on the outbreak of the Second World War.
“In 1978, The Wyre Lady was brought to Doncaster where she continued to trade having carried near on two million passengers over the course of her life.
“We are disappointed that someone would want to cause such damage and are urging anyone with information that could help our investigation to come forward."
If you have any information that can help with our enquiries please call 101 quoting incident number 745 of 25 June 2020.”