CARE has been responding after the Labour Party said it was wrong for young fans to be exposed to betting ads.
With 25 of the 92 league clubs, including nine out of 20 Premier League sides, currently engaged in such sponsoring, shadow Digital, Culture, Media and Sport (DCMS) secretary Tom Watson said it was time to take action.
"Football has to play its part in tackling Britain's hidden epidemic of gambling addiction. Shirt sponsorship sends out a message that football clubs don't take problem gambling among their own fans seriously enough.
"It puts gambling brands in front of fans of all ages, not just at matches but on broadcasts and highlights packages on both commercial television and the BBC.
"Just as tobacco companies were banned from sponsoring sporting events and putting their logos on branded goods because of the harm smoking can cause, it's right that we recognise the harm problem gambling does and take gambling logos off football shirts."
Mr Watson said clubs should take the lead from the Football Association as it ended its commercial agreement with Ladbrokes in June after deciding it was not appropriate for it to partner with a gambling company.
Supporting the calls, CARE's Director of Parliamentary Affairs Dr Dan Boucher said: "This is a positive step in the right direction".
"Betting ads on sports shirts are irresponsible - it normalises gambling to a very young audience."
"Shown completely without context, these shirts are on the backs of children's sports heroes and create the illusion that gambling is harmless, fun and without consequences. We know that is not the case. There has been a trebling in problem gambling amongst 18-24 year olds."