Steven Emerson issued an apology for his "terrible error" made on Fox News.
Mr Emerson, who founded a group called The Investigative Project on Terrorism, was giving his perspective on the terror attacks in France.
Birmingham Children's Hospital said it hoped Mr Emerson had learned "what a fantastic city Birmingham is."
"The money he has donated will go towards improving the lives of thousands of patients and their families who are treated at our hospital each year," a statement from the hospital said.
Children's Hospital donation idea
The suggestion Mr Emerson could donate to Birmingham Children's Hospital came from hyperlocal news blogger Luke Addis, who runs Birmingham Updates.
He said he came across Mr Emerson's video and comments on a social media feed on Sunday night and emailed the commentator for a response.
"I thought his comments were absurd," he said.
"I love that our city is diverse and wouldn't change it."
When Mr Emerson responded with an apology and mentioned he intended to make a donation to a charity, Mr Addis suggested the children's hospital.
Mr Emerson's comments attracted widespread ridicule, with the hashtag #FoxNewsFacts trending on Twitter.
He admitted he had "made an egregious error here in not doing my homework", adding: "I deserve what I got."
He said he had relied on sources he had used in the past, but accepted "responsibility" for his comments and did not know how his reputation would be affected in the long term.
More than 3,500 people have signed an online petition calling for Mr Emerson to make an "on-air apology to the people of Birmingham UK for saying non-Muslims cannot enter our beloved multi-cultural city".
Maryam Snape, who started the petition, said: "The fact of the matter is the American people saw this story and they are still going to believe it is the truth until he puts it right."
An American commentator who called Birmingham a "Muslim-only city" where non-Muslims "don't go" has donated £500 to the city's children's hospital.