The state's health department confirmed the new infections on Monday, as active infections rose to 1691 cases.
Tasmania's previous daily case high of 428 was reported on Saturday.
Fifty-six cases are being cared for at community case management facilities and 278 are being managed at home.
COVID-positive hospital cases have dropped from three to two. None are in intensive care.
Some 120 people were released from isolation on Saturday after recovering from COVID-19.
Health Minister Jeremy Rockliff said a three-year-old child had tested positive for COVID-19 in the state's south, after presenting to Royal Hobart Hospital's emergency department.
"While no doubt distressing for the family, the child was treated by an emergency department medical specialist and was deemed safe for discharge," Mr Rockliff said in a statement.
Rapid antigen tests remain available to asymptomatic close contacts or anyone directed to take a test by the health department, he added.
But acting state opposition leader Anita Dow said testing capacity was "crumbling", contact tracing had been "abandoned" and COVID@home calls were going unanswered "for hours".
Tasmania Premier Peter Gutwein will provide further information at a press conference scheduled later in the day.
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