Communications teams were working to reassure staff at Royal Alexandra Hospital in Paisley after it became a major focus of scrutiny.
Two men aged 25 and 28 from the hospital's staff accommodation were detained on Monday. The hospital was also treating one of the two men who drove the car into the terminal building at Glasgow airport. He was reported to be in a critical condition.
NHS Greater Glasgow and Clyde director of communications Ally McLaws said: 'Our communications team launched an immediate internal exercise to reassure staff, and through them patients and visitors.'
A representative of the Scottish branch of Unison said: 'Local branch representatives are talking to members and managers to keep them abreast of the situation.'