The news of the sixth death came as Premier Daniel Andrews and Health Minister Jill Hennessy announced a $500 million funding boost for the state's ambulance services.
The package - which the government says is in addition to $144 million provided in the 2016/17 budget - will result in 450 new paramedics being employed over three years.
Labor also plans to establish six new "super response centres" across Melbourne to meet a growing demand driven by population growth.
"We know that in an emergency every second counts," Hennessy said in a statement on Sunday.
"That's why we're giving our paramedics the new resources they need, where they are needed most."
Monday's asthma storm overwhelmed emergency services and hospitals.
Paramedics dealt with an unprecedented 1900 emergency calls in five hours on Monday evening as the phenomenon swept the state.
At one point there were 140 code one cases occurring at the same time.
Melbourne hospitals across Monday and Tuesday treated more than 8500 patients.
- AAP