Bruno Kahl said his agency was aware of cyber attacks with no other purpose than "causing political uncertainty".
"Europe is in the focus of this attempted disruption, and Germany in particular," he told Sueddeutsche Zeitung.
Russia or groups linked to Russia have been regularly accused of such attacks.
Campaigning has yet to start for federal elections in autumn 2017 but Angela Merkel announced last week she would be seeking a fourth term as chancellor.
She told reporters that hacking attacks were now becoming commonplace and people should not allow themselves to be annoyed by them.
She was speaking after a cyber attack on Sunday left 900,000 Deutsche Telekom customers with their broadband service cut off. The German government has not yet blamed any group for the hack but says "it's hard to tell the difference between criminal activities from a particular state and state activities".
"Such cyber attacks, or hybrid conflicts as they are known in Russian doctrine, are now part of daily life and we must learn to cope with them," Mrs Merkel said.
The hackers used malware to target Taiwanese-made Speedport routers and German officials say the attack could have been far worse if the routers had not crashed. "We were lucky this time - the attack didn't work properly," said Arne Schoenbohm of Germany's federal office for information security.
If they had succeeded, the infected routers could have formed a network known as a "botnet" for attacks on websites known as Distributed Denial of Service (DDoS).
Why is Russia suspected?
Earlier this year, Germany's domestic intelligence agency accused Russia of being behind a series of cyber attacks on German state computer systems, including targeting the lower house of parliament last year.
A group known as Fancy Bear, which is thought to be linked to the Russian state, has been blamed for the attacks. It is also believed to have targeted Mrs Merkel's ruling Christian Democratic Union party.
In October, the US formally accused Russia of trying to interfere with its presidential elections by attacking political organisations. The Kremlin has consistently denied such allegations.
On Tuesday, Mr Kahl said of Washington's assessment: "Attributing to a state actor is technically difficult. But there is some evidence that this is at least tolerated or desired by the state,."
Mr Kahl has been in his post for nearly five months and has rarely spoken in public in that time.