The student was found with the makeshift weapon last Friday and officers from West Midlands Police are investigating.
It follows a similar report that saw a 12-year-old boy cautioned at another Birmingham school on 11 November.
"These appear to be isolated offences," said Insp Beth Bridges.
"I want to reassure people that this isn't something that we're seeing on a daily basis.
"We encourage parents to speak with their children about the dangers and consequences of carrying weapons, and be vigilant.
"Unfortunately these makeshift items have been seen elsewhere in the country in the past and we want to send a strong message that it is illegal to carry such weapons."
A highlighter pen with a pencil sharpener blade attached to it was confiscated from a boy at a Birmingham school, police have said.