His comments come amid reports three of the professional dancers have not been vaccinated.
Speaking to reporters in Washington DC, Mr Johnson said: “I think that that’s a matter for the producers, but I strongly believe that people should get vaccinated.
“I don’t want to bully people or to lecture them but, well I don’t mind lecturing them, I’ll lecture them. I think it is a great thing to do for yourself, your family, your community.
“I think people should get a jab and it is a wonderful thing to do.”
The first live show of the series will go ahead as planned on Saturday night despite the controversy.
The BBC has said it is following all government guidelines to ensure the show can be made safely.
A spokesperson for the show said they could not comment on whether the BBC or the production team knows the vaccination status of the professional dancers.
As was the practice last year, the professionals formed a bubble before the start of production so they could record the group routines.
Each dancer will then form a bubble with their celebrity partner so they can compete in the live shows.
Great British Bake Off star John Whaite, actor Greg Wise, soap star Katie McGlynn and Olympian Adam Peaty are among the line-up for the 2021 series.
The Sun has reported three professional dancers are unvaccinated.
Former professional dancer James Jordan, who appeared on the show from 2006 to 2013, has said they should not be allowed to take part.
He told ITV’s Good Morning Britain: “I definitely believe they don’t deserve their right on the show and the celebrities have every right to refuse to dance with them.”
He added on Twitter: “Just a quick one to all the anti-vaxxers out in force tonight.
“Thank your lucky stars for the 44 million people in this country that did get vaccinated, so you are now able to go back to work and get back to some kind of normal.”
A spokesperson for Strictly said: “We do not comment on speculation of somebody’s Covid vaccination status.”