Manchester United, Liverpool, Arsenal, Chelsea, Tottenham and Manchester City announced they have signed up for the new competition, and will be joined by teams from Italy and Spain.
The move would see them create a competition for up to 20 clubs to rival the Champions League, but would not feature relegation or promotion.
Teams would play each other in midweek while still competing in their domestic leagues.
The Prime Minister posted his views on Twitter on Sunday evening, criticising the prospect of six English clubs possibly joining a breakaway continental league.
“Plans for a European Super League would be very damaging for football and we support football authorities in taking action,” said Mr Johnson.
“They would strike at the heart of the domestic game, and will concern fans across the country.
“The clubs involved must answer to their fans and the wider footballing community before taking any further steps.”
Scottish Conservative leader and part-time assistant referee Douglas Ross also voiced “serious reservations” about the creation of a European Super League.
Speaking on BBC Breakfast Ross on Monday, Mr Ross said: “I think there have been many concerns raised by the government, by UEFA and others. I think there are serious reservations about what's been proposed.
“It would have a massive affect for football and there is a real danger that fans of the Premier League which is one of the most success leagues anywhere in the world, would be left with a lot poorer product at the end of this.
“I understand why certain clubs are appealing for this, but overall it would be a deeply regrettable move.”
The mooted shake-up was widely criticised by political leaders including Culture Secretary Oliver Dowden.
Uefa, the football associations of England, Spain and Italy, plus the Premier League, LaLiga and Serie A have also spoken out against the move.
Mr Dowden described fans as the “heartbeat of our national sport” and said any major decisions about a European league “should have their backing”.
“With many fans, we are concerned that this plan could create a closed shop at the very top of our national game,” he said.
“Sustainability, integrity and fair competition are absolutely paramount and anything that undermines this is deeply troubling and damaging for football.”
Labour leader Sir Keir Starmer said the plan “cuts across all the things that make football great”.
“It diminishes competition. It pulls up the drawbridge. It is designed for and by a small elite. But worst of all, it ignores the fans,” he said.
European Commission vice president Margaritis Schinas said: “We must defend a values-driven European model of sport based on diversity and inclusion.
“There is no scope for reserving it for the few rich and powerful clubs who want to severe links with everything associations stand for.”
Fans’ groups, including those linked to Liverpool, Spurs and Chelsea, have also voiced their opposition to the clubs joining a super league.