His departure comes after three other members, who held the board's leadership positions, stepped down on Monday. The scandal has already cost the USAG sponsors and heavily damaged its reputation.
"I joined the board just nine months ago, well after Nassar's departure from USAG, in the hopes of helping to move the organization in a positive direction," Martinez said in an emailed statement. "That hope for this board is no longer possible so I submitted my resignation."
Nassar, 54, was sentenced to 40 to 175 years in prison on Wednesday for sexually assaulting young girls under the guise of medical treatment, following a weeklong hearing that saw more than 150 accusers recount their stories in a Michigan courtroom.
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He is already serving a 60-year federal sentence for child pornography convictions and faces a final sentencing next week in Michigan for three additional counts of abuse.
USAG's spokeswoman, Leslie King, did not respond to requests for comment on Thursday. In a statement on Wednesday, the federation said it supported the USOC letter but did not specifically address the call for board members' resignations.
The webpage listing USAG's board members appeared to have been taken down around midday on Thursday without explanation. Most of the remaining 17 board members contacted by Reuters either declined to comment or did not return requests for comment.
The USOC itself has not escaped criticism from some of the sport's biggest names.
"I have represented the USA in two Olympics and have done so successfully," gold medallist Aly Raisman, who accused Nassar of abusing her, said at his hearing. "And both USA Gymnastics and the U.S. Olympic Committee have been very quick to capitalise and celebrate my success, but did they reach out when I came forward? No."
Lou Anna Simon, the president of Michigan State University, where Nassar also worked, stepped down late on Wednesday night amid calls from critics and Michigan lawmakers for her termination.
"As tragedies are politicized, blame is inevitable. As president, it is only natural that I am the focus of this anger," Simon said in her resignation letter.
On Thursday, U.S. senators Richard Blumenthal, a Democrat, and Jerry Moran, a Republican, wrote a letter to USOC, USAG, Michigan State and the National Collegiate Athletic Association, demanding information on whether the institutions failed to investigate reports of Nassar's abuse.
More than 140 victims have filed lawsuits against USAG and Michigan State.
(Additional reporting by Joseph Ax in New York and Steve Friess in Lansing, Michigan; writing by Jon Herskovitz; editing by Gareth Jones and Cynthia Osterman)
