More than 1800 travellers came to Tasmania last weekend despite Premier Peter Gutwein implementing an arrivals form last Friday and making it clear they were not welcome.
A government spokesman said that up until Sunday midnight 1841 Tasmanian Arrivals Forms had been filled out.
The form aims to help keep track of visitors to enforce self-isolation.
Coronavirus: All the latest updates on COVID-19 for Tasmania
Coinciding with concerns on social media Mr Gutwein has ordered extra TT-Line sailings to transport visitors north across Bass Strait and has given tourists until April 1 to leave caravan parks.
"Yesterday my expectation was clear - that unless you are a returning Tasmanian or an essential traveller, you should not come to our state given our strong border restrictions to keep Tasmanians safe and secure," he said.
"I have directed TT-Line to prioritise its bookings to ensure that only Tasmanians returning, freight and those travellers who have met essential traveller or exemption criteria, are able to travel.
"Any non- essential travellers, including Tasmanians, who do return will be subject to the 14 day self-isolation period as is currently the case.
"TT Line will also contact all mainland caravan and motorhome bookings and advise them that if they don't have a permanent address in Tasmania, they will not meet the self-isolation rules."
TT Line, along with Biosecurity Tasmania and Tasmania Police, are enforcing the 14 day self-isolation requirements.
Social media has been rife with stories of vehicles with interstate number plates driving off the Spirit and heading to supermarkets rather than into self isolation.
Many Facebook subscribers are calling for a total lockdown to prevent COVID-19 infecting the general community.
Tasmania has 47 confirmed cases, all of which have been directly or indirectly linked to overseas travel.
Acting Deputy Commissioner Jonathan Higgins said no one had been charged by police under the Emergency Management Act.
"Tasmania Police has officers embedded in the Covid Response Unit to follow up reports of non-compliance," he said.
"The CRU is receiving a large number of reports and each report is triaged. Where necessary, the Police Compliance Team is tasked to undertake a visit to the quarantined person.
"Police have conducted well over 200 checks on people in quarantine across the state since 6pm Wednesday and yesterday to 3pm Thursday."