Officials did not identify the individual, and said they were still looking for tips that could further the investigation.
"We have at least two search warrants we need to serve in order to gather enough evidence to take him from person of interest to suspect. Once those warrants are served and we gather the appropriate evidence, we will make his identity available as quickly as possible," police spokesman Tanner Tixier told reporters.
When asked whether it was too soon to say authorities "have your guy," Tixier said yes. He did say that the person in custody matched the description of a suspect given out earlier in the day.
Two vehicles were cutting each other off Tuesday afternoon on westbound Interstate 40 in Albuquerque, according to Officer Simon Drobik, another police spokesman.
The sole gunman, one of the drivers, pulled up to the vehicle carrying the girl and opened fire, Drobik said, citing information given by the girl's father.
Killed was Lilly Garcia, said Mayor Richard Berry.
The father was driving a red pickup and had just picked up Lilly and her 7-year-old brother from school. The children sat in the back seat, police Chief Gorden Eden said. The mother wasn't in the car, police said, correcting an earlier account.
The gunman is believed to have been the only occupant of his vehicle, Eden said.
"There were two children in this truck that this animal decided to open fire on just because he happened to get cut off on the freeway," said Tixier, the spokesman.
Investigators were still trying to determine the number of shots fired.
"The information that we received from the father was that he heard multiple shots," the police chief said.
The father pulled over his vehicle upon finding his daughter bleeding. He gave her first aid.
"To have your child in your hands in such circumstances is going to live with the father for the rest of his life," Eden said.
A total reward of $26,000 has been offered, authorities said. The mayor's office and the City Council each offered $10,000, the FBI $5,000, and Albuquerque police $1,000.
What exactly provoked the gunfire remained unclear Wednesday. "Some type of incident happened," the police chief said.
Officials expressed shock at the shooting.
"I have never seen it before," Eden said of the shooting. "I've seen tragic loss of children in car crashes. To me this is one of those crimes which is unexplainable."
"I just can't express how sad it is to know that something as simple as going down the freeway and your child dies because of road rage," Gov. Susana Martinez said, according to CNN affiliate KRQE
Said Mayor Berry: "The Garcia family is in the thoughts and prayers of our community and our nation. The senseless murder of four year old Lilly Garcia has broken our hearts and cut to the core of our community.
"Make no mistake; this act of violence will not go unanswered," Berry said in a statement.
The suspected shooter was driving a maroon or dark red, four-door Toyota sedan, possibly a Corolla or Camry from 2014 or 2015, police said Wednesday.
The suspect's sedan was "sportier" with dark tinted windows and a spoiler on the trunk, and the car has a gray University of New Mexico license plate with the Lobo logo on the left hand and may contain the digits "200."
Tixier said investigators believe that vehicle is in a garage they hope to search.
The suspect was described as a man in mid-20s to early 30s, with short dark hair, possibly in a fade haircut, and with a thin manicured goatee around his mouth, police said.
The suspect was wearing a black shirt with gold or yellow writing on it, and his race is white with a dark complexion, possibly Hispanic. The suspect has a thin face, soft jaw and average build, police said.
Police had to shut down momentarily that two-mile stretch of freeway to look for shell casings and other evidence, Drobik said.
Police found no helpful evidence from a review of a camera footage taken by the New Mexico Department of Transportation, Drobik said.
"Again we are begging for the community's help. This should have never happened. This is a complete disrespect for human life," the chief said at a press conference. "We're starting to see this throughout our nation, and this is something that should not be happening."
Homicide detectives were scheduled to interview the girl's family members, Drobik said.
A Bernalillo County sheriff's deputy was passing by the family's disabled red pickup and was the first on the scene, Drobik said.
An off-duty nurse from the University of New Mexico Hospital and a second nurse happened to be passing by and stopped to give aid, police said.
The girl was rushed to that hospital in an ambulance, escorted by police, Drobik said.
Detectives said the suspect probably fired off shots while driving, KRQE
No one else was injured in the shooting, police said.