Mr Reiter said: “We are now talking of course even more intensively with the security authorities and the police about the subject of Oktoberfest.”
Three savage attacks all took place within the same week in Bavaria.
An Afghan refugee hacked 19 people on a train with an axe and a knife on Monday 18 July while a shooting in Munich left nine dead on the following Friday.
Mohammad Daleel tried to gain entry into the Ansbach Open music festival but was turned away before detonating his bomb just moments later.
The Munich mayor added: “We will need to consider whether to prohibit backpacks. I say this quite openly, because since Ansbach everyone will have to understand that we need to think about such measures.”
He said: “It is a really bad time. A great depression has overcome the population in Bavaria.”
Oktoberfest attracts more than six million visitors into the German region each year.
Police are likely to be out in force after a heightened terror alert was issued by Angela Merkel in the wake last week’s attacks.