The incident occurred at around 03:30 on Saturday local time in the city’s entertainment district.
Indianapolis police say officers found the three men with gunshot wounds and they were taken to nearby hospitals.
The Dutch defence ministry said one of the men was in a critical condition and that the other two were conscious.
It said all three were members of the Commando Corps, one of the special operations units in the Netherlands armed forces.
The shooting occurred during their free time in front of the hotel where they were staying, the ministry added.
Local police said they believed there had been an earlier altercation between the men and another person or group.
Speaking to FOX59, an officer with the Indianapolis Metropolitan Police Department said: “Right now the information we’re willing to disclose is that it was not something that occurred inside the hotel.
“It was a previous altercation we believe at another location.”
The Dutch defence ministry said the men’s families had been informed and that an investigation by local police was under way.
No arrests have been made.