Prime Minister Manasseh Sogavare said this now brought to 12 the number of students who had contracted the coronavirus there.
All had been asymptomatic.
The latest six are from a group of 144 students scheduled to be on one of two repatriation flights next week.
They had undergone the first of three tests before the flight.
The Solomon Star newspaper reported the results were received by the government on Tuesday.
Sogavare said students who had tested negative were staying in two hotels while waiting for repatriation flights on 27 and 29 September.
Over 300 students from the Solomons have been studying in the Philippines.
There have been over 200,000 cases of the Coronavirus there while Solomon Islands have no confirmed cases.