The French Open finalist, Verkerk suffered a 3-6, 6-1, 6-4 loss was eliminated in the first round for the third time in five appearances at this event.
Making his Dutch Open debut, the 26-year-old Galimberti captured the Rome challenger in May and is playing in just his fourth ATP event in 2003.
Verkerk, nursing a shoulder injury, said he would have an MRI on his shoulder on Wednesday.
A second upset was posted by Frenchman Jean-Rene Lisnard, who knocked off No. 2 Gaston Gaudio of Argentina, 6-0, 7-6 (7-5).
Third seed and defending champion Juan Ignacio Chela beat fellow Argentine Mariano Puerta, 6-3, 6-1.
No. 6 Raemon Sluiter bounced Germany's Alexander Waske, 6-4, 6-3.