CAIR said Rose Hamid's eviction from the rally in South Carolina sent a "chilling message to American Muslims".
Ms Hamid was removed after making a silent protest on Friday.
Mr Trump's proposed ban on Muslims entering the US has been widely condemned.
During the rally in the town of Rock Hill, Ms Hamid stood up wearing a T-shirt bearing the words: "Salam, I come in peace" - "Salam" is the Arabic word for peace.
When she stood up, the crowd around her began chanting "Trump! Trump!" as they had reportedly been instructed to do in the event of any interruption, reports the BBC's Anthony Zurcher from Rock Hill.
Ms Hamid, a 56-year-old flight attendant, was then told by a security officer that she had to leave. She was booed as she was escorted out.
CAIR said that as well as apologising to Ms Hamid, Mr Trump should "make a clear statement that American Muslims are welcome as fellow citizens and as participants in the nation's political process".
Mr Trump has yet to respond.
At a Republican presidential forum in nearby Columbia,  on Saturday morning, Ohio Governor John Kasich condemned the way the Trump crowd handled the protest.
"We don't need to be shouting and booing and scaring somebody," Mr Kasich, who is competing against Mr Trump for the Republican presidential nomination, told the BBC. "This is not some high-school basketball game. We are all our brother's keeper."
He added that the next US president must be willing to work with moderate Muslim nations.
"That may not win me the Republican primary, but there's more to life than that," he added.
The Council on American-Islamic Relations (CAIR) has urged Republican presidential hopeful Donald Trump to apologise to a Muslim protester ejected from one of his rallies.