The Clarets were leading 1-0 at half time courtesy of Ben Mee's goal before the match was called off during the interval.
Photographs showed apparent crowd trouble at Turf Moor, with police holding back Hannover fans from Burnley supporters.
"Today's game has been abandoned, on Police advice. Burnley Football Club will issue a statement on today's events following a full de-brief later today," read a statement on the club's official Twitter account.
Burnley boss Sean Dyche added: "They called us in and said, 'Look, we're going to call it for the safety of all involved, stewards, fans, police etc'. That was pretty early. The police were in the referee's room, called me, went through the procedure, and obviously we fully support the police's decision.
"Hopefully nobody has got hurt. You can't really tell what's going on from how far away we are, but it didn't look ideal. You hope that's gone out of the game and it generally has. The police called it early. No-one wanted anything other than a game of football."
Burnley begin the new season away to champions Chelsea next Saturday.