British acts are no longer guaranteed visa-free travel in the EU and face large fees to tour in some countries.
Many, including Sir Elton, have warned the restrictions could "threaten the future success of British music".
Lord Frost said the government would benefit from their assistance.
He said it would be "extremely helpful" if musicians and music industry bodies could "use their relationships" within the EU "to encourage those governments to be less restrictive".
"I said that to Elton John and I will say it to others," he told a committee of MPs on Tuesday. "We need that sort of help and support, and I'm convinced it would make a big difference to help improve the situation."
Lord Frost was speaking to the House of Commons culture select committee, who had called him to give evidence on post-Brexit visa arrangements for workers in the creative industries.
Labour MP Clive Efford poured scorn on his suggestion, asking whether the government's policy boiled down to "getting ambassadors to lobby [foreign governments] and asking Elton John to get his mates to ring people up?"
"I wouldn't be so dismissive of such activity," replied Lord Frost. "That is how you make things happen in diplomacy."