Three unrelated shootings since Christmas Eve included a man being injured in Shipley, a car damaged in Huddersfield and a police vehicle being shot on Christmas Day in Bradford.
West Yorkshire Police said the incidents were being taken "very seriously".
No one was seriously injured.
The first incident happened in Market Square, Shipley, at about 04:00 GMT on Saturday.
One man is thought to have been shot but not seriously injured after a collision between a vehicle and pedestrian.
In the second incident, a car was damaged in Bradley Mills, Huddersfield, at 15:10 on Saturday.
A car, thought to be a black Mercedes, drove down Harpe Inge carrying people wearing masks. One person got out and a firearm was discharged, police said.
Another car, thought to be a grey Mercedes, was shot. No one was injured.
In the early hours of Christmas Day, a police vehicle windscreen was shot on Sackville Street in Bradford.
Officers had been called to reports of an assault and at about 04:40, while speaking to the victim, a shot was fired at the windscreen.
No one was injured by the firearms discharge but one person was injured as a result of the assault and a 19-year-old man has been arrested.
While the firearms incidents are not linked, they are being taken "very seriously" and witnesses should contact West Yorkshire Police.
Assistant Chief Constable Russ Foster said: "Despite this recent spate of gun-related crime, the chances of becoming a victim of such an incident in West Yorkshire are very low."
Last January, 80 illegally-held guns were taken in West Yorkshire in a weapons surrender which is due to be repeated in the new year.
Police in West Yorkshire are "very concerned" by an "unprecedented" level of firearms incidents over Christmas.