The worker flew into the Solomons with about 80 other Chinese nationals, many of whom will construct stadia for the 2023 Pacific Games.
The Covid-19 Oversight Committee said the worker passed a package to a Chinese national outside of quarantine, who owns a hardware store in Honiara.
The Solomon Times reported that person had now been quarantined at the Pacific Casino for 14 days.
The Ministry of Health said it was continuing to investigate the breach.
On Tuesday, Solomon Islands Prime Minister Manasseh Sogavare said the workers were being quarantined under strict conditions.
Because the flight originated in China, there was widespread public outrage over the decision to accept it but Sogavare said it was approved after careful assessment of the risks involved.
All the passengers are being isolated until they are deemed safe to release, he said.