The foal's body was found at the edge of a waterhole.
The pair who discovered the body said it appeared the foal had been shot in the gut and there was evidence it had been lassoed.
The condition of the body indicated the foal had died some time before the muster, which is targeting up to 2000 horses.
The bureau said it had completed its investigation, which included input from a veterinarian from the US Department of Agriculture.
"An Animal Health Inspection Service veterinarian with more than 30 years experience performed a field examination of a dead colt located near Gilman Springs and concluded that the bony skeletal remains of the four to six-week-old colt showed no detectable physical trauma," the bureau said.
"The time of death was approximately one month ago or prior, and the carcass was completely desiccated and in advanced stages of decomposition.
"There were random holes of various sizes that were evidence of feeding by scavenger birds, according to the veterinarian. Due to advanced stages of decomposition, the cause of death could not be ascertained."
A bureau special agent accompanied the veterinarian and found no physical evidence on or near the carcass to indicate that it had been shot or killed in that location.
The muster, which began on August 11, has so far gathered 592 horses from the range, with two deaths reported. Both deaths were the result of euthanasia, both due to pre-existing injuries.
An aerial survey of the Twin Peaks area in late July found more than 2000 horses and more than 200 burros.
The bureau says it aims to leave about 450 horses and 72 burros in the area, comprising nearly 800,000-acre.
The bureau said the first 32 animals had been returned to the range.
Ken Collum, manager of the Eagle Lake Field Office, said the first group of 27 stallions and six mules was released today back into the Skedaddle and Dry Valley home ranges.
The first group of 14 mares is scheduled to be released tomorrow, after treatment with a long-term fertility control vaccine.
"We are pleased by the progress to date," said Nancy Haug, the bureau's northern California district manager.
"When you're working with hundreds of wild horses that can weigh well over a thousand pounds, there is always an element of risk to both the horses and the people conducting the roundup. There have been no injuries to personnel and no serious injuries to horses."
Haug said horses gathered to date had come from the south end of the herd management area, where water is typically sparse in the summer.
She said the area was being monitored to ensure the horses didn't run low on water before being mustered.
"That didn't happen and there is more water as we move further north."
Water supplies will be adequate for horses being returned to the range, she said.
The operation is expected to continue into September.
Wild horses and burros have been transported to the Litchfield Corrals where they will be prepared for adoption, expected to be October.
Wild horse advocates, including the Cloud Foundation, have criticised the muster and expressed alarm at the number of bureau operations to remove wild horses from the western rangelands.
They have been vocal in their criticism of the bureau's strategy which has seen a growing number of wild horses held in captivity. That number now stands at about 36,000.
The Humane Society of the United States has also voiced its concern, saying it opposed the roundup of wild horses as a primary management strategy when more humane and fiscally responsible strategies, such as fertility control, were readily available.
"The US Bureau of Land Management has not made the case that the California horses are creating any significant ecological imbalance," the society's California senior state director, Jennifer Fearing, said.
"As such, the agency should halt the gather at once and place an immediate moratorium on any remaining gathers scheduled for this year until it completes and presents Congress with a sustainable, long-term wild horse management plan."
The society said any proposed plan presented to Congress for consideration must include: