In an email to staff on Tuesday morning, Niall Sookoo, Labour's election and campaign director, said the party's "robust security systems" had defended the "integrity" of their data.
In a statement, Labour said it took "swift action" and its security systems were not successfully breached.
Labour said it reported Monday's incident to the National Cyber Security Centre - a part of intelligence agency GCHQ which monitors and works to protect security systems.
Commenting on the news, Corin Imai, senior security advisor at DomainTools, said: "This should be a significant concern to all voters in the United Kingdom regardless of their political viewpoints".
British security services had warned that Russian Federation and other countries could use cyber attacks or divisive political messages on social media to attempt to disrupt the December 12 election.
A spokeswoman said: "We have experienced a sophisticated and large-scale cyber-attack on Labour digital platforms. It just means organizations need to be one (or four) steps ahead of the attackers".
The Labour leader, addressing media during a campaign event in Blackpool in the north-west of England on Tuesday, voiced his concern at the timing of the cyber attack.
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In a letter sent to the party's campaigners, Niall Sookoo, the party's exec director of elections and campaigns, said: "Yesterday afternoon our security systems identified that, in a very short period of time, there were large-scale and sophisticated attacks on Labour Party platforms which had the intention of taking our systems entirely offline".
Britain's security agencies have warned that Russian Federation and other countries could use cyberattacks or political messages on social media to attempt to disrupt the December 12 election.
In a DDoS attack, hackers flood a target's online platforms with traffic from various sources, with the aim of slowing down access or causing websites to crash.
However, subsequent reports have suggested it was actually a DDoS attack. The "Russia" report was produced by Parliament's Intelligence and Security Committee and submitted to the Prime Minister's office on 17 October 2019. "Mitigation techniques are available and worked in this case", a NCSC spokesman told Reuters.
The nature of such attacks often makes it hard to attribute responsibility to any particular group, he said.
The report was sent to Downing Street but needs further approval before it is released to the public, the government has said.
"Every person who votes in this country deserves to see that report before your election happens".