United were handed a €300,000 ($336,420) fine for "minor break even deficits" for the financial years spanning between 2019 and 2022.
Barca, meanwhile, were issued a larger €500,000 ($560,700) fine "for wrongly reporting, in the financial year 2022, profits on disposal of intangible assets (other than player transfers) which are not a relevant income under the regulations," UEFA said in a statement.
FFP was introduced by UEFA in 2009 to prevent football clubs from spending more than they earn in pursuit of success and risking their long-term financial health as result.
AC Milan, Inter Milan and Paris Saint-Germain -- who were fined by UEFA in September -- all met their stricter financial targets for last season. They will continue to be monitored for compliance over the next year.
UEFA has updated the FFP rules that were approved in 2009 with a new monitoring system. It prioritises financial sustainability for clubs and moved away from setting competitive balance on the field as an achievable target.
Information from the Associated Press contributed to this report.