Premier Peter Gutwein has urged businesses impacted by new nation-wide restrictions on non-essential gatherings to heed by the rules and close at midday today.
Prime Minister Scott Morrison announced late on Sunday pubs, registered and licensed clubs, gyms, indoor sporting venues, cinemas, entertainment venues, casinos, night clubs and places of worship would be closed today.
Bottle shops are excluded and restaurants and cafes can stay open for takeaway or delivery only.
Coronavirus: All the latest updates on COVID-19 for Tasmania
Mr Gutwein said he did not want to see people come together for "last drinks" as was seen when the United Kingdom announced it would be shutting its venues.
"We need to act now," Mr Gutwein said.
"This cannot be a migration from the pub to the backyard.The rules of social distancing apply.
"If you are in doubt close and seek advice. Tasmania Police will be policing this."
Mr Gutwein said he expected all Tasmanians to play their part in curbing the spread of coronavirus.
"We are at at war against an insidious disease. Social distancing is the weapon that we have," he said.
"There is no community transmission at this stage but we have to do everything we possibly can to beat this disease.
"The failure of people to do this, the failure of people to do this and follow the law, will put people's lives at risk.
"Whilst we will review these [measures] on an ongoing basis we should expect these measures to be in place for six months."
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Mr Gutwein said new rules for aged care facilities would also come into effect from today.
"There will be restricted access to aged care facilities from 12 noon today," he said.
"There will be some exceptions for people providing care and support.
"[Visitors] only up to two people for a maximum of two hours unless it's for end of life support."
People under the age of 16 are not allowed to visit unless attending for end of life support.
Tasmanian schools will stay open but where parents and carers want to keep their children at home they can do that, the Premier said.
"Children at home must be at home," Mr Gutwein said.
"This does not mean take your children home and let them go on holiday.
"The best and most safest place for your children is at school, that is the advice. If you decide to take them out of school, look after them."
Term dates will remain the same but the Premier said the situation would be reviewed at the school holidays.
There are now 22 cases of the virus in Tasmania, including the first two cases in the state's North-West.
Public Health director Mark Veitch said five new cases were diagnosed yesterday.
"There were two people who had returned from the United States, one from the Ruby Princess ... and one from another cruise the Ovation of the Seas," Dr Veitch said.
Dr Veitch said about 250 Tasmanian residents on a number of cruise ships which docked in Sydney in recent days were being contacted by Public Health to make them aware of their quarantine restrictions when returning to Tasmania.
The impacted ships are the Ovation of the Seas which docked on March 18, the Voyager of the Seas which docked on March 18 and the Celebrity Solstice which docked on March 19.
Dr Veitch said people could be trusted to self-isolate.
"It's like vaccination. We focus on people who don't vaccinate. It's very important we focus on the positive," Dr Veitch said.
But Labor leader Rebecca White said more needed to be done and called for the government to act decisively and close schools and non-essential services.
"Now that there's a social security net in place to support people to stay home the government should close schools," Ms White said.
"There's governments across the world who regret not taking actions earlier."
Greens health spokeswoman Rosalie Woodruff said there was a mixed message across the country on school closures.
"The conversation is about keeping schools open because that's the normal space but it's not a normal environment anymore. There's nothing normal about being in school for teachers, students and their parents," Dr Woodruff said.
"I'm saying that I don't understand that this situation can be sustained for very long."