"Given the incident, Linda Ramirez-Sliwinski is stepping down as a delegate and will be replaced," said Obama spokeswoman Amy Brundage.
The incident occurred Saturday, when two children were playing in a tree next door to Ramirez-Sliwinski's house.
She said the parents were outside supervising the children, but she went over and told them to get out of the tree because she was concerned about the boys' safety and because the small magnolia tree was being damaged.
The father of one of the boys told her it was none of her business, she told the Chicago Tribune, and "I calmly said the tree is not there for them to be climbing in there like monkeys."
The mother of one boy called police.
Cmdr. Michael Kilbourne said Tuesday a ticket was issued because the ordinance bans conduct that disturbs or alarms people. One of the boys told police he was scared by her comment and a mother said she was disturbed, he said.
Ramirez-Sliwinski does not have a listed telephone number. She did not respond immediately to an e-mail.
Ramirez-Sliwinski says she doesn't plan to run for another term on the village board. "In the eyes of the public, this is wrong," she told the Arlington Heights Daily Herald.