Rachel Reeves, who chairs the Business Select Committee, wrote to both bosses after they faced heavy criticism of their treatment of employees.
Mr Martin told more than 40,000 Wetherspoons staff that they would not be paid from Friday until the government made clear how it intended to cover staff costs through a new job support scheme.
Mr Ashley angered Sports Direct staff by telling them they had to come into work at branches despite a government order for people to stay at home wherever possible.
The company had initially told staff that shops would remain open after the lockdown came into force on Monday night. After a public backlash stores were closed but staff were told they still needed to come in.
During Prime Minister’s Questions on Wednesday Boris Johnson said Mr Ashley and other company bosses should “obey the rules” or “expect the consequences”.
Ms Reeves said it is “crucial that companies such as JD Wetherspoon and Sports Direct do all they can to ensure their workers are properly protected and get the pay to which they are entitled”.
In a letter to Mr Martin, Ms Reeves asked for “detailed information about the measures that Wetherspoons is taking to support its employees during the current coronavirus crisis”.
She added: “This is a national emergency, and governments, citizens and businesses are taking unprecedented measures to protect lives and livelihoods.
“I was therefore disappointed to read that you have not indicated whether you intend to cover the wages of your staff until government support comes through.
“This is despite other companies in your industry guaranteeing that they will pay their staff for at least eight weeks.
“Furthermore, you also seem to have suggested that when the government do pay 80 per cent of your staff’s wages, you might not pay the other 20 per cent.
“Finally, I am deeply concerned that while you encourage your workforce to consider working for supermarkets, you note that if they do, you will give them ‘first preference’ if they ‘want to come back’.”
The committee’s questions include:
* How many of your staff will be furloughed?
* Will you pay your staff’s wages up until the government’s money comes through?
* Will you pay the remaining 20 per cent of your staff’s wages when government support begins?
* How you will pay and treat staff that you employ who are on zero hour contracts?
* Will your staff have to reapply for their jobs when the present crisis is over?