The 23-year-old has been arrested on suspicion of being the owner or person in charge of a dog dangerously out of control causing injury.
A 24-year-old woman was previously arrested and has been released on bail.
The arrests relate to incidents on April 20 and 26, in which a seven-year-old boy and two men were attacked in South Kirkby, near Wakefield.
The boy needed surgery on his upper arm and shoulder. They happened on Mill Lane, Mill Close and Holmsley Avenue.
Despite the arrests, the dog is yet to be traced.
West Yorkshire Police is continuing to appeal to anyone with information about its whereabouts and is asking people to remain vigilant. It has been described as being an Alsatian breed or similar.
Anyone with information is asked to either call 101 or use 101 Live Chat on the West Yorkshire Police website quoting crime reference 13220211431.