The actor, from Port Talbot, wants to put an end to placing homeless teenagers into "unsuitable" bed and breakfast accommodation.
Instead, they should be supported by the "fantastic network of charities" across Wales that can provide a safe place, he said.
The Welsh government said more than half Welsh councils do not use B&Bs.
The online petition has attracted more than 19,000 supporters.
It comes as the End Youth Homelessness Cymru partnership claimed more than 100 teenagers aged 16 and 17 in Wales were accommodated in bed and breakfasts during 2013-14.
Placing young person in bed and breakfast accommodation puts them at an "unacceptable risk", it added.
Mr Sheen said: "Being a teenager is a difficult and confusing time but being a teenager and homeless leaves you dangerously vulnerable.
"We should do everything we can to provide a safe shelter for them and not put them in circumstances where they are at even further risk."
The petition adds: "All we are asking for is that homeless teenagers have a place of safety, a shower, a hot meal and someone to talk to. I don't think it's too much to ask of our government this Christmas."
A Welsh government spokeswoman said: "Research undertaken by the WLGA in November revealed over half of Welsh councils were not using B&Bs for 16 and 17-year-olds.
"We are working on strengthened statutory guidance to eliminate the use of B&Bs for young people in the remaining local authorities and strongly encourage them to learn from councils who are already identifying alternative safe and secure accommodation for young people facing homelessness."
Michael Sheen has launched a petition calling on the Welsh government to help homeless teenagers in Wales.