A Sporting Equals audit found 26 of 601 board members - just over 4% - are from BAME backgrounds.
Only two of 68 chairpersons or chief executives are BAME.
"Talking to other athletes and sportspeople, they are expressing concern that it is a world not open for them," said Briton Ohuruogu, 32.
"They won't be welcomed, won't be valued and it is very negative. They have gone as far as they can as athletes but they don't feel there is any more room for them to go."
Shadow sports minister Rosena Allin-Khan told BBC Sport that "greater representation" was needed in boardrooms to "increase role models".
The Labour MP for Tooting added: "It is about empowering people who are already at the top of their game and those who have finished their sporting career and want to take up a position in the boardroom."
Sporting Equals works to promote ethnic diversity in sport, and its audit included responses from grassroots sports organisations funded by Sport England and some institutions funded by UK Sport.
Taking into account the UK BAME population of 14%, it revealed:
Wasim Khan was the first Britain-born Pakistani to play professional county cricket, and was part of Warwickshire's double-winning side in 1995.
In 2014, Leicestershire made him the first BAME chief executive of a county cricket club.
"There is still a huge amount of work to be done but, for the first time, we have seen some real positive work," he told BBC Sport at a Sporting Equals event in London.
"One of the excuses thrown is that there is not enough talent in the BAME community but that will be addressed now.
"This is not based around tokenism; this is on merit. We want people to have a competitive chance of getting into sport."
Khan said he had to "break the mould" as a youngster but said change is now taking place.
For the first time, England's cricket team have four Britain-born Muslims in their side - Moeen Ali, Adil Rashid, Haseeb Hameed and Zafar Ansari.
Khan added: "In terms of diversity, you can see it is starting to happen in cricket and they are leading the way.
"We need to make sure more are making it into leadership positions because there are enough role models now."

MiHomecare had not been paying employees to travel between clients, meaning their hourly rates of pay did not comply with the legal minimum.
Richie Lewis, of the Unison union, said the firm was "rectifying systemic errors" and valuing its staff.
MiHomecare said it had taken steps to ensure there were no future problems.
Unison said, typically, care providers do not pay their employees to travel between clients and Mr Lewis urged other companies to review pay procedures.
"Home carers work long hours under increasingly difficult conditions and it is often the case that they end up out of pocket in order to provide the level of care that their clients need," he added.
MiHomecare, which operates Village Home Care, employs 6,000 home care workers in England and Wales who look after 10,000 elderly, disabled and infirm people.
The company, said it had completed a comprehensive review of payments for all of its care workers "to be absolutely certain that they are treated fairly and that we comply with wage legislation".
"We have found some errors in calculating travel time pay and we have decided to make a one-off payment to all affected people," a spokeswoman said.
"Additionally we took steps in June 2015 to ensure that this should not be an issue in future by revising some pay rates and amending care rosters."
Barriers exist for black, Asian and minority ethnic people entering sports administration, says former Olympic and world 400m champion Christine Ohuruogu.
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About 100 home care workers in Swansea and Carmarthenshire are to be paid up to £2,500 each after a company breached minimum wage rules.