City have been given 90 days by European football's governing body to pay the fine, with Liverpool and Tottenham Hotspur also disciplined.
Tottenham have been served with a €20,000 fine for kicking off the first leg of their last-16 tie against RB Leipzig late, with Jose Mourinho held responsible for the delay.
Liverpool, meanwhile, have been served with a €3,250 fine for setting off fireworks during the second leg of their last-16 tie with Atletico Madrid.
City's fine is understood to relate to the logo of official gambling partner Marathon Bet being too large on the players' pre-match training top.
According to article 29.02 of Uefa's guidelines, sponsor logos on non-playing attire can only be a maximum of 200cm².
The €3,000 fine is nothing compared to the two-year ban and €30m penalty handed to City by Uefa last month, though is unlikely to help heal an already-strained relationship.
City were banned from all Uefa competitions in February after they were found to have misled European football’s governing body and broken Financial Fair Play rules.
The Premier League champions will appeal against Uefa's decision at the Court of Arbitration for Sport this summer, though their hearing is likely to be delayed by the coronavirus pandemic.