Money will be given to other projects, and potentially county football associations, if changes are not made, she told BBC Radio 5 live's Sportsweek.
Crouch said: "I'm not shy to say to the FA 'if you don't reform your governance structures, I will give that money to other bodies that deliver football'."
She said the governing body receives £30m to £40m of public funding.
Earlier this month, former FA chairman David Bernstein said the organisation was "outdated" and needed reform.
"We have a massive problem in this country at the centre of English football. I'm talking about an outmoded structure which is not modern enough and not independent enough," he said.
Asked about his comments, Crouch replied: "I share David's frustration. That's why we've made it clear that all sports governing bodies have to reform their governance codes.
"The FA is not excluded from that, and if they don't, they won't get public funding. It's as simple as that."
A report from the Commons Culture, Media and Sport Committee in 2013 called for reforms in English football - and outlined concerns including financial management as well as the balance of power between the Premier League and the FA.
Crouch said there was good work being carried out by association executives but problems revolved around the FA Council, which has 124 elected members.
"If there's no move whatsoever, and at the moment we are seeing nothing from the FA in terms of progress, they are likely to lose some public money or it will go elsewhere in the delivery of football," she added.
The FA declined to comment, although a source stressed that it is a not-for-profit organisation with government funding ploughed into grassroots football.

Labour asked for the data to be released to Parliament.
The government blamed "unacceptably lax" contracts that allow staff to re-join the NHS a month after redundancy.
It says it's working on tough new plans to cap payouts, and has reduced administrative posts overall.
Labour shadow health secretary Andy Burnham said it would be galling for nurses who were battling over pay to see, as he put it, cheques handed out like confetti.
Auditors have previously reported that the average payout was £43,000.
The number of national health service staff estimated to have been made redundant and later re-employed almost doubled in the last year - from 2,200 managers - Ministerial responses to Parliamentary Questions have revealed.
The total now stands at 3,950.
Overall, more than 10,000 full-time workers were made redundant from the NHS in England since the restructuring of the service.
Changes introduced in April 2013 have seen 150 primary care trusts, run by managers, replaced with 211 clinical commissioning groups, led by family doctors.
Health Minister Dr Dan Poulter said: "By reducing managers and administrators by over 21,100, we are freeing up extra resources for patient care - £5.5 billion in this Parliament and £1.5 billion every year thereafter."
The FA could lose millions of pounds of funding if it does not reform, says Sports Minister Tracey Crouch.
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New figures indicate that almost 4,000 staff made redundant from the NHS in England, before last year's major restructuring, have since been re-employed.