Oliver Dowden said coronavirus "certificates" were being considered as a way of getting people back to larger events "in significant numbers".
Fans are set to return to sporting events, in limited numbers, from May 17, subject to further reviews, as a part of the government's four-step road map out of lockdown, which could see all legal limits on social contact lifted by June 21.
The FA Cup final and World Snooker Championship will be among a group of sporting and cultural events used as pilots to test the large-scale return of spectators to venues.
The government announced plans for a pilot programme to begin in April when it set out its road map in February for the easing of coronavirus restrictions, and the Department for Digital, Culture, Media and Sport (DCMS) said there will be "around a dozen" events serving as tests in total.
"From June 21, if all goes to plan in the way that I described, we hope to get people back in significant numbers," Dowden told Sky News.
"We're piloting the different things that will enable that to happen - clearly it will have to be done in a Covid-secure way.
"You would expect, and we will be testing these things, things like one-way systems, things like masks, things like hand hygiene and everything else.
"Another thing that we are considering is a Covid certification, and we will be testing whether we can use Covid certification to help facilitate the return of sports."
He added that final decisions had not yet been made and that he was working with Cabinet Office Minister Michael Gove, who is leading a review on this.
Dowden said current social distancing measures make it "very, very difficult" for smaller indoor events to go ahead.
"I hope we will be able to find ways of mitigating against certainly having the sort of social distancing that we have at the moment," he added.
"The sort of social distancing we have at the moment makes it very, very difficult, for example, for theatre productions to be run profitably.
"It makes it very, very difficult for our football clubs to run profitably if you have to have those large distances between people.
"Clearly, we have been in the situation for the past year where we have had to have those distances, so we are proceeding with caution, that's why it's the last stage, that's why we are piloting different ways of mitigating against that."