Mr. Wilansky, who spoke by telephone and checked details with his daughter as he did, said the explosion had taken place around 4 a.m. Monday, when most of the protesters were gathered around a bonfire near the foot of the bridge.

Image Sophia Wilansky was injured while protesting against the Dakota Access Pipeline in North Dakota this week. Credit... via Wayne Wilansky

His daughter and a handful of others were farther up on the bridge, he said, “playing around,” using pieces of plastic and wood as sleds to skid across icy sections of the highway, when an officer began firing foam or plastic bullets at her and another person.

“She was backing away as they were shooting her,” Mr. Wilansky said, adding that someone from the police lines then threw a device, which he called a grenade, that hit her in the forearm and exploded.

Lt. Tom Iverson of the North Dakota Highway Patrol offered a different version of the episode, which he said was being investigated by the North Dakota Bureau of Criminal Investigation and the federal Bureau of Alcohol, Tobacco, Firearms and Explosives.

Around the time of the explosion, Lieutenant Iverson said, officers fired sponge and beanbag rounds at three people who had shielded themselves behind a length of plywood near a burned vehicle on the bridge. The three were thought to be acting suspiciously and refused orders to emerge, he said.

Officers saw someone roll metal cylinders to the protesters by the burned vehicle, Lieutenant Iverson said, and then heard an explosion. Afterward, he said, several protesters ran up, pulled a woman from under the vehicle and ran off. Three propane canisters were recovered from the vicinity of the explosion early Tuesday, he said.

Lieutenant Iverson said that officers did not use concussion or flash grenades at any time. Instead, officers used tear gas, pepper spray canisters and what are known as stinger balls, round grenadelike objects that spread tiny rubber pellets to try to disperse protesters, he said.