The 34-year-old, who made 207 appearances for the club, said he appreciated the success of the Government's vaccine programme, but said passes were a step too far.
There are plans to trial Covid passports at upcoming sporting events, including the FA Cup final on May 15, which could host 20,000 fans.
It comes amid suggestions there could be a lower vaccine take-up in minority communities.
In response, Wolves legend Ikeme tweeted: "I would urge the Football Association not to use Covid passes in the up and coming FA Cup finals.
"Covid passes will be a form of discrimination in which you have said you stand against.
"It will cause even more discrimination in the communities a lot of players are bending the knee for, before games.
"This will not bring more people into our beautiful game – it will simply push them away.
"And in engaging with Covid passes, you are complicit in pushing for this in society. The game is either safe for us all, or none of us."
I would urge @FA not to use covid pass in the up and coming FA cup finals . Covid passes will be a form of discrimination in which you have said you stand against!! It will cause even more discrimination in the communities a lot of players are bending the knee for before games !— Carl Ikeme (@Carl_Ikeme) April 6, 2021
Ikeme, who retired from playing in 2018 after being diagnosed with leukaemia, believes Covid passports would cause division in society.
He said: "We know black and ethnic minorities are more hesitant to have vaccines.
"I think it will create a bigger divide. I don’t believe communities who have their own personal choice not to have a vaccine should be discriminated against even further than they have been throughout the years.
"It’s going to create more divisiveness in our society than there is already. Having these Covid passes is either going to force people to have a jab they don’t want or is going to force people not to take part in society the way we’re all used to.
"And everyone who lives in this country has a fundamental right to live by their own beliefs. The vaccine programme has been a success in a really difficult year and it is starting to protect the most vulnerable, but I think the vaccine passport is a step way too far.
"The Government knows it would cause more discrimination and I think the FA knows it would cause more discrimination, that’s why I’m urging them not to take part in it. Football players have been bending the knee all year against discrimination and this will affect ethnic communities even more."