Ms Hennessy said at the 2010 election the former coalition government promised a new public hospital in Geelong and instead delivered a private facility.
"That's meant that in Geelong we've had three private hospitals effectively competing for the market share," she said.
"Things have been very challenging in the private hospital sector."
The Geelong site is owned by Barwon Health, which also provides public services from the facility.
Ms Hennessy said Barwon Health would continue to operate from the site and staff cut from Healthscope could apply to work in the public system.
The two hospitals will be closed over the next four weeks, Healthscope said.
"We conducted an exhaustive evaluation of alternatives but unfortunately it is simply not viable to continue operations into the future," chief executive Gordon Ballantyne said.
The government will work with Healthscope and other private providers to make sure scheduled elective surgery operations go ahead.
The Andrews government has not ruled out taking over the Geelong facility entirely.
No public services are provided At Cotham hospital.
"It is a much smaller site, but there are still about 100 people that are going to be looking at what their future employment opportunities are," Ms Hennessy said.
"For those at Cotham we'll make sure that all of our state services support those staff."
The Australian Nursing and Midwifery Federation will hold members meetings on Wednesday with affected nurses.