Stephanie said the conditions at the Park Spring Road warehouse - which employs thousands of people, many of them from the local area - also flouted government guidelines on social distancing.
“I have spoken to a number of concerned workers employed at the ASOS warehouse in Grimethorpe who feel that their health is being put before profit in this national crisis,” she said.
“ASOS employs more than 4,000 workers in the UK. They shouldn't have to put theirs and their family’s wellbeing on the line for a paycheck.
“I have written to the chief executive expressing my concern and will do all I can to make sure workers across Barnsley East are able to do their jobs in safe conditions.
“We should treat workers in London and the north the same.”
A spokesperson for site manager XPO Logistics said: "We’re supporting our colleagues by adhering to UK Government and Public Health England guidance.
"As the situation evolves, all appropriate health and safety measures are being put in place, alongside regular two-way communication, which ensures staff are kept informed and we’re listening to any concerns they may have."