One in five small firms say a cyber attack has been committed against their business in the two years to January 2019.
More than seven million individual attacks are reported over the same period, equating to 9,741 incidents a day.
The annual cost of the attacks is estimated to be £4.5bn, with the average cost of an individual attack put at £1,300, said the report.
Victims are most frequently subject to phishing attempts, with 530,000 small firms suffering from such an attack over the past two years.
Hundreds of thousands of businesses also report incidences of malware (374,000), fraudulent payment requests (301,000) and ransom-ware (260,000).
Those based in the North West, South East and West Midlands are most likely to be the victims of cyber attacks, the study indicated.
Martin McTague of the FSB said: “These findings demonstrate the sheer scale of the dangers faced by small firms every day in the digital arena.
“The issue of business crime is overlooked too often, even more so of late in this climate of sustained political uncertainty and inaction. Meaningful steps must be taken to safeguard our small firms, and by extension the wider economy.
“The Government should be doing more to tackle this scourge by enhancing the current policing response, including investing more in cyber upskilling for police personnel as part of its wider recruitment push.”
“Banks also have a role to play. They should be building in as much resilience as possible into banking and payments systems, and made liable for the losses of business – not just consumer – customers when they fall victim to cyber crime.
“Software providers could also be doing more. Government should be prepared to step in and require automatic patching and updates to be the default option for all software products.”
Last year the National Cyber Security Centre said that more online attacks are being launched against UK businesses than ever before, while insurance provider Hiscox said the majority of businesses suffered a cyber attack of some sort in 2018.