Queensland police have fined a Melbourne couple who tested positive to COVID-19 on the Sunshine Coast more than $4000 each for allegedly lying on their border declaration passes.

The couple allegedly travelled to Queensland via Goondiwindi on June 5 after having been in Victoria.

The pair entered the state when the Victorian capital was in lockdown.

Police allege the pair deliberately provided false information to obtain a Queensland border declaration pass.

Authorities were later alerted to the pair after the woman, 44, tested positive to coronavirus on June 9, sparking a major contact tracing effort across south-east Queensland.

The man, 48, also tested positive the following day.

The pair were interviewed by police after being released from hospital, where they were undergoing treatment for COVID-19.

They were each issued with a $4003 fine for failing to comply with a COVID-19 border direction.