The FFP rules are designed to prevent European clubs from spending more than they earn and getting into financial trouble in pursuit of success.
UEFA did not provide any specific details of the alleged wrongdoing in its statement.
Manchester City 'welcomes' investigation
The Premier League champions responded to the probe with a statement on their website.
"Manchester City welcomes the opening of a formal UEFA investigation as an opportunity to bring to an end the speculation resulting from the illegal hacking and out of context publication of City emails," it read.
"The accusations of financial irregularities are entirely false. The Club's published accounts are full and complete and a matter of legal and regulatory record."
UEFA did not give a timetable for the case and said it would have "no further comment while the investigation is ongoing."
Club already broke rules once
Manchester City were previously found guilty of breaching FFP rules in 2014 and fined €60 million ($72.6 million at the time). However, €40 million of that amount was returned to the club in 2017 after UEFA confirmed it had complied with its sanctions.
Any club found guilty of breaching FFP can be barred from the lucrative and prestigious Champions League.
Manchester City, who face German club Schalke in the second leg of their round of 16 tie on Tuesday, are desperate to win the competition.
Football clubs’ spending spiraling out of control?