Chelsea will issue stadium bans to parents or guardians who allow their children to go on to the pitch.
Leeds United have introduced similar measures in response to young fans running on to the pitch after full-time to speak to players or ask for shirts.
A young supporter ran on to the pitch towards goalkeeper Kepa Arrizabalaga following Chelsea's home Carabao Cup semi-final first leg on 5 January.
Chelsea said "lengthy stadium bans" await those who breach regulations.
A club statement said: "Chelsea Football Club wishes to remind supporters that encroaching onto the pitch before, during or after matches is a criminal act and can result in serious punishment for the club, fans and, in the case of minors, their parents or guardians."
It added: "In the case of minors entering onto the playing surface, the parent or adult ticket holder accompanying them is deemed responsible for their actions and will also receive a ban from attending future matches."
Chelsea said the ground regulations at Stamford Bridge "have never been more important" than during the pandemic, as the pitch and touchline areas form part of the matchday red zone which seeks to minimise the spread of the virus.
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