The Brazilian model will "develop, promote and participate in global initiatives" before the Women's World Cup kicks off in Australia and New Zealand this summer.
Former FIFA council member Moya Dodd has described the move as "tone deaf".
The former Australia international said: "When a girl plays football, the world sees her differently.
"Instead of being complimented on her nice looks or her pretty dress, she is valued for her game-saving tackles and brilliant goal-scoring.
"She's admired for what she can do, rather than how she looks, putting her on a more equal footing with her brothers in a way that can alter the whole trajectory of her life's ambitions.
"In a FIFA World Cup year, that's the message that should be ringing loud and true around the world. Where a supermodel fits into this is truly baffling."
Dodd, who served on the committee for Australia and New Zealand's winning bid to host the World Cup, feels that Lima's public image is an "odd fit for an organisation that says it wants to empower girls and women".
She added in a LinkedIn post: "I asked whether the FIFA ambassador will be delivering messages on body image, wellbeing and healthy eating.
"What will this ambassador represent to the large and growing population of aspirational #womensfootball players and fans who love the game because (it) shows us what empowerment and equality can look like?"
FIFA president Gianni Infantino is supportive of Lima's appointment as she "lives and breathes 'futebol'".