Mr Clark said it was "important" to follow through with the decision to invest in the high-speed railway despite criticism from the former foreign secretary.
In an interview with the Sunday Times, Mr Johnson suggested pausing the scheme so a high-speed link could be built across the north of England instead.
Middlesbrough-born Mr Clark, who was asked about his former Cabinet colleague's remarks during a fringe event at the Conservative Party conference in Birmingham, said: "I think it would be completely the wrong approach.
"One of the upsetting criticisms, I think, of successive governments in the UK is that we haven't got on and invested in supporting infrastructure for the economy. "We've made a decision to invest in HS2 - I think it's important that we follow through with that."
Phase 1 of the railway will open between London and Birmingham in December 2026.
A second Y-shaped phase will launch in two stages. Phase 2a from the West Midlands to Crewe will begin in 2027, followed by Phase 2b from Crewe to Manchester, and Birmingham to Leeds, in 2033.
In his interview, Mr Johnson said: “There are projects we should have on transport in the north of the country that ought to take precedence over HS2. It’s crazy how long it takes to get east-west across the country."
Earlier this year, northern political and business leaders called for high-speed rail linking the region’s biggest cities should be delivered at the same time as HS2
MPs, civic leaders and company bosses claim delivering Northern Powerhouse Rail (NPR) at the same time as HS2 would be a major step to narrowing the North-South divide, opening up much larger potential labour markets for businesses and enhanced leisure and social activities for families.
One leader has also said it could help heal the political disillusionment held by many Northern voters.
Mr Johnson's comments came as Transport Secretary Chris Grayling today marked the start of HS2 construction work during a visit to the site of the future high speed railway station in Birmingham.
Curzon Street station in central Birmingham will be the first intercity station built in Britain since the 19th century and will open in 2026.
Mr Grayling said: “Today is an important moment in the history of rail travel in the UK. Britain was the inventor of the modern railway and seeing the start of work on the first railway to be built north of London for over 100 years is an incredible moment for the future of this country.
“HS2 will not only deliver the step change in rail travel that this country needs, it will also ensure that Britain is at the forefront of railway construction once again. Supporting thousands of jobs and businesses and creating a first class skills base that we can export around the world.”
Henri Murison, Director of Northern Powerhouse Partnership said: “HS2 is a vital scheme for the whole country – increasing much needed capacity with the West Coast mainline already not able to keep up with growth since it was improved with a Â£9 billion ten year upgrade.
"In Leeds, the South Bank redevelopment next to the HS2 station is expected to provide 35,000 jobs across the financial, professional, creative and digital sectors and 4,000 homes with the arrival of companies like Sky demonstrating the increase in confidence is already supporting economic growth.
"The business community of the North and the country, as represented by organisations such as the Northern Powerhouse Partnership and British Chambers of Commerce, stand fully behind the scheme.
“It is just not good enough to make any suggestion we can only have Northern Powerhouse Rail if HS2 is cancelled because the country needs both, and it is unhelpful for Boris Johnson MP to suggest otherwise.
"Practically, the two schemes are completely interlinked, with the tunnel which will allow those from Yorkshire and the North East to reach Liverpool the same infrastructure which will allow HS2 trains from Manchester Piccadilly to go South towards Birmingham and London through the Manchester Airport station.
"His further ‘idea’ that a bridge to Northern Ireland to grab headlines will be embraced by the North in place of commitments the government has already made and is starting in the case of HS2 to build and deliver, and which have support from the Labour opposition, is just not going to happen.”