Bikes or cars made before 1960 will no longer have to undergo the inspection under plans.
The current requirement for the vehicles to be tested annually goes beyond European legislation, according to the Department for Transport.
A spokesman said: “As part of the Government's commitment to cutting unnecessary red tape, today's proposals would exempt private vehicles manufactured before 1960 from the MoT test, reducing costs for owners.”
Announcing the plans, Penning said: "We are committed to reducing regulation which places a financial burden on motorists without providing significant overall benefits.
"Owners of classic cars and motorbikes are enthusiasts who maintain their vehicles well - they don't need to be told to look after them, they're out there every weekend checking the condition of the engine, tyres and bodywork.
"That is why I am today putting forward proposals to scrap the MoT test for these vehicles - this will result in savings for the Government and for motorists."
A consultation on the plans runs until January 26: www.dft.gov.uk/consultations.