The Mid Yorkshire Hospitals NHS Trust, which runs Pinderfields, Pontefract and Dewsbury Hospitals, said the problem was an added stress for its staff.
The government acknowledged on Monday there was a shortage of personal protective equipment (PPE) for frontline NHS staff, but business secretary Alok Sharma said plans were in place to remedy that.
But the trust's chief executive, Martin Barkley, said he didn't know when more gowns would be arriving.
It follows an intervention by local MP Yvette Cooper on Tuesday.
Ms Cooper, who represents Normanton, Pontefract and Castleford, said she'd spoken to frontline nurses about the "struggles" they're facing with a lack of protective gear.
Mr Barkley said: "The shortage of long-sleeved disposable gowns has been a major concern at the Trust for almost a week.
"We are unsure when our next delivery will be, and this creates a very stressful situation for our staff.
"The trust has been doing absolutely everything we can to secure gowns, including ordering alternative garments to try and ensure our staff have the protective clothing they need.
"We are grateful for the support of Yvette Cooper, and indeed our other local Members of Parliament, in this endeavour."
All hospital patients being treated for COVID-19 from the Wakefield district and Dewsbury are being treated at Pinderfields Hospital.
Chemotherapy services as well as elderly patients being treated for other conditions have been diverted away from Pinderfields for the meantime to minimise the risk of infection.
In an interview at the end of last month, Mr Barkley said that supplies of some PPE had fallen to "concerningly low" levels in the days after lockdown was imposed on the UK.
Local Democracy Reporting Service