The incident was detected last Wednesday, a day before Canada's signals intelligence agency said network operators of critical infrastructure should boost their defenses against Russian state-sponsored threats.
"Critical services ... are currently functioning. Some access to internet and internet-based services are currently not working," said a statement from the Treasury Board, which has overall responsibility for government operations.
"There is no indication that any other government departments have been impacted," it said, adding no more details would be released.
Neither the Treasury Board nor the foreign ministry responded when asked whether Russian actors were responsible.
Canada has taken a strong line against Russia's military build-up on the Ukrainian border strong line against Russia's military build-up on the Ukrainian border.
Ottawa rarely speaks about hacks into its systems. In 2011, officials said "a highly sophisticated Chinese state-sponsored actor" had broken into a leading research body. Beijing denied it.
In 2014, a former Canadian cabinet minister said Chinese operators were suspected of hacking into the Treasury Board and the finance ministry in 2011.
(Reporting by David Ljunggren; Editing by Howard Goller)