Mr Constance said inner west drivers would continue their employment under the privatised new operator.
The drivers' absence comes the morning after Transport for NSW applied for an urgent hearing in the Industrial Relations Commission to challenge the planned strike, which was due to start at 12am Thursday.
The government will continue to own Region 6 buses and assets, including depots, and set Opal fares and timetables.
But Bob Nanva from the Rail, Tram and Bus Union has denied that bus services are to blame for late services and instead pointed the finger at Sydney's wider traffic congestion woes.
Drivers will walk off the job from midnight Wednesday with the depots in Leichhardt, Tempe, Burwood and Kingsgrove involved in the action, leaving the inner west and large parts of southern Sydney without buses.
A map provided by the union showed the strike will impact a huge chunk of the city, from Sans Souci to Silverwater and from Glebe to Strathfield, encompassing important arterial roads and the Anzac Bridge.
"Minister Constance needs to understand that you can not treat the community and public transport workers with such contempt", he said.
However, Mr Constance told reporters, the members have shown "contempt for a court ruling" and should "go straight back to work".
"We are sourcing a fleet of buses to operate a more limited service in the areas of highest demand". "This call for a strike is about union bosses putting themselves before customers, egged on by the Labor party", he said.
The union says the decision reneges on a deal made only in December for the government-owned State Transit to run services for the next five years. I would urge Mr Preston to do the same.
"They would tell me to get nicked", Mr Preston said, candidly referring to how the drivers would respond if asked to work at such late notice.
"Members of the public should make alternative arrangements to travel to work and take their children to school", RTBU spokesman Chris Preston said.
438 and 461 will be available along Parramatta Road between 6am and 10am and 3pm and 7pm.