Arsenal say anyone caught "throwing objects and use of pyrotechnics" could also receive sanctions
Arsenal fans who enter the field of play in future home games will be issued with bans and membership cancellations by the club.
Two supporters got on to the pitch in Thursday's Carabao Cup semi-final second-leg loss to Liverpool.
A third person was also stopped as they approached celebrating Reds players.
"In recent matches at Emirates Stadium, there have been a number of people who have entered the pitch," Arsenal said in a statement.
"We strongly remind everyone it is a criminal offence under the Football (Offences) Act 1991 to enter the pitch without prior permission.
"If anyone is thinking of doing this please refrain, as all football clubs and the police are taking this matter extremely seriously.
"All perpetrators of public order offences, which includes pitch encroaching and other recent incidents of throwing objects and use of pyrotechnics, will receive lengthy stadium bans and further possible legal sanctions."
Arsenal are next at home against struggling Burnley on Sunday.
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Source: bbc.com