A morning training session was called off as players underwent tests to determine whether the virus may have spread among the group.
But there were no positives detected and that meant Koeman's charges could train in the evening, ahead of playing Wednesday's match against Athletic Club.
A club statement read: "In accordance with LaLiga protocol, the FC Barcelona first-team squad undertook PCR tests on Tuesday morning. All tests came back negative."
The Camp Nou giants said on Monday that two members of the first-team staff had returned positives for coronavirus, and sports and health authorities were informed about those results.
Koeman's team sit fifth in LaLiga ahead of their trip to the Basque Country to play Athletic, who are ninth.
Barcelona, who are 10 points off the top of LaLiga, have won the previous two matches on their travels after going four away league games without a win.