The woman aged in her 70s was taken to hospital by ambulance on Friday night but died about 9am Saturday after being ramped at the emergency department, the union representing Tasmanian paramedics said.
She could not receive appropriate care in what was a distressing situation for the patient, her family, and paramedics, Health and Community Services Union industrial manager Robbie Moore said.
"I don't think any Tasmanian would be happy to hear that a person, an older Tasmanian, is not able to get a hospital bed when they need one," Mr Moore told AAP.
"It's a reasonable expectation that we'd be able to access our health system. The government should absolutely be ashamed this is the situation they have let it get to."
The Tasmanian Health Department told the ABC a formal review into the woman's death was underway.
AAP has contacted the department for comment.
The Tasmanian Greens said the woman's death showed the significant stress the state's hospitals were under.
"The lives of Tasmanians depend upon the Liberals taking action," the party's health spokesperson Rosalie Woodruff said in a statement.
Mr Moore said ambulance ramping is an ongoing issue for the island state, with Tasmanians not receiving appropriate care and paramedics unable to respond to urgent jobs because they're stuck at hospitals.
The state government needs to open more hospital beds immediately, he said.
"In the longer term, they're meant to be negotiating with all their staff when it comes to their wages and conditions," Mr Moore said.
"We need them to pay competitive wages with the mainland to ensure that we have adequate staff to provide the health services that Tasmanians need."
Meanwhile, the Tasmanian branch of the Australian Nursing and Midwifery Federation is continuing strike action on Wednesday over pay and conditions.
Premier and Health Minister Jeremy Rockliff last week offered a deal to the union in a bid to stop the strike but union members voted to continue the action.
"While the offer does provide positive measures for the medium to longer term, the main concern from members is that it doesn't provide tangible solutions immediately," the federation's Tasmanian secretary Emily Shepherd said.
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