Ben Mee opened the scoring four minutes before half-time for the hosts at Turf Moor but violence flared in the David Fishwick Stand, where the visiting supporters were located, during the interval.
Hannover fans clashed with stewards, tore off seats and threw them towards Burnley supporters and, after a long delay, the decision to call off the game on safety grounds was made.
Burnley tweeted: "Today's game has been abandoned, on police advice."
Burnley manager Sean Dyche later voiced his support over the decision to abandon the contest.
"They [the police] called us in and said, 'look, we’re going to call it for the safety of all involved, stewards, fans, police, etcetera'," Dyche said, as quoted by the Burnley Express.
"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."
Mee appeared to gesture towards the Hannover fans, urging them to calm down, after he scored and Dyche felt his defender's actions did not inflame the situation.
"To be fair, I think Ben was innocently saying 'calm down', I've looked at the footage," he added. "He's a solid citizen."
Burnley are set to offer a full statement on the events that led to the abandonment later on Saturday, following a full debrief.