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Mr Corbyn said the estimated £162m cost would be paid for by an increase in tax on private health insurance premiums.
The plan was backed by NHS unions.
But a Conservative spokesman said: "This promise isn't worth the paper it's written on because Jeremy Corbyn simply wouldn't be able to deliver it."
The Labour leader announced the plan during a visit to nursing students in Worcester.
He said hospital parking charges "place an unfair and unnecessary burden on families, patients and NHS staff".
"Our hospitals are struggling from under-funding at the hands of Theresa May's Conservative government, but the gap should not be filled by charging sick patients, anxious relatives and already hard-pressed NHS staff for an essential service."
The Unison union says some hospitals are charging staff, including nurses, nearly £100 a month to park.
Labour says increasing the tax rate on private health premiums from 12% to 20% would raise an additional £377m.
It says that three quarters of private insurance policies are taken out by employers "on behalf of wealthier, high skilled employees".
Unison general secretary Dave Prentis said: "The cost of hospital parking is heaping excessive financial pressure on health employees who've gone for years without a decent pay rise."
A Conservative Party spokesman dismissed the proposal as unworkable.
He said: "With Corbyn in charge of our Brexit negotiations, the economy and our NHS would be at grave risk. There would be less money to spend in hospitals, not more."
A Liberal Democrat spokesman said: "Only the Liberal Democrats are being honest with the public about the need to all chip in a little more to rescue the NHS and care."