Hillary said that she is "monitoring the horrific situation in Munich".
"We stand with our friends in Germany as they work to bring those responsible to justice," she tweeted.
The President of Germany, Joachim Gauck, said that he was "horrified" by the shooting in Munich.
In a statement, Mr Gauck said: "I am with all the victims in my thoughts and all those who are mourning or fearful for loved ones."
He also offered his "solidarity" to people in the emergency services who are working this evening, trying to "protect people and save lives".
Speaking to German television ARD, Chancellor Angela Merkel's chief of staff, Peter Altmaier, said the possibility of a terrorist attack had to be considered
"We don't rule out any possibility. I was in close contact with the Bavarian interior minister all afternoon and evening. The Chancellor is being kept up to date at all times and everything we know and can say so far is that it was an inhuman, cruel attack. Our thoughts are with the victims of this attack. We can't rule out a terrorist connection, we can't confirm this but we investigate in this direction as well," he tweeted.
According to the Sueddeutsche Zeitung newspaper, GSG9 -- an elite German counter-terrorism unit -- is now involved in the operation in Munich.
However, the police have not confirmed this.
Munich Police are now reporting a ninth death. They said that the police are investigating whether this person was involved in the attack.
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