Sammy Pacheco, 51, was working on the tower near Little Water when a 60-foot section of the steel structure fell over and crushed much of his body.
Pacheco still was in critical condition Wednesday at San Juan Regional Medical Center, hospital spokeswoman Kathryn Pettijohn said.
Pacheco's family members waited outside the Intensive Care Unit on Wednesday, but declined to comment on Pacheco's condition.
"Our thoughts and prayers are with the Pacheco family," said Deenise Becenti, spokeswoman for the Navajo Nation Tribal Utility Authority.
NNTUA is being investigated by NNOSHA, as well as the New Mexico OSHA and federal OSHA. The utility authority hired L&B Telecommunications LLC to build one of its cell phone towers, despite L&B's history of mishaps.
"This is not the first time we've dealt with L&B," said NNOSHA Director Julius Elwood, who did not say how many citations L&B has received from NNOSHA. L&B did not return calls Wednesday evening for comment.
This is by far the worst incident the Mississippi-based company has been involved with, Elwood said.
NNOSHA is getting help from other OSHA agencies because L&B is not a tribal company, though NNTUA is an extension of the Navajo tribe.
"We're running into some obstacles, so they are helping us," said Elwood.
While perhaps the first of its kind on the Navajo Nation, the incident is hardly isolated. Cell tower injuries and deaths are being reported increasingly nationwide.
"Apparently, it's an epidemic throughout the nation. Unfortunately, we've become part of that statistic," Elwood said.
Elwood estimates that approximately 700 towers are spread across the more than 27,000 square miles of the Navajo reservation.
The towers are owned by a variety of companies, including Verizon, AT&T and CellularOne. None were involved in Sunday's incident.
CellularOne CEO Louise Finnegan said she has gone through tower-climber training herself to understand the process. "It's pretty rigorous," she said.
The most dangerous part, construction of the towers themselves, is where most accidents occur, Finnegan said, which is why her company is so stringent about training.
"It's without question the most dangerous phase," Finnegan said.
Pacheco was injured when a section of the tower was being lifted by crane onto an already-placed section.
Pacheco was on the tower when part of it toppled over after the crane failed to fully lift the piece over the other section. He fell about 40 feet to the ground.
"We don't know all the details," NNOSHA's Elwood said.
Pacheco was the only one reported injured. He was transported to San Juan Regional Medical Center via Air Care on Sunday.
Elwood said a report on the investigation will be completed as soon as NNOSHA is able.
"We're still trying to piece things together," said Elwood.