Mohammed Siddique, 60, and his son Mohammed Waqar, 24, admitted wilful cruelty to a child under 16.
The four attacks took place at the Jamia Mosque in Sparkbrook, Birmingham, between May and June 2014, Birmingham Crown Court heard.
The pair, from the Tyseley area of the city, also face a teaching ban.
Sam Forsyth, prosecuting, said the victim was beaten with a plastic stick and given back-of-the-hand slaps by each of his tutors for "talking in the classroom" at a Birmingham Islamic centre.
The boy was hit during four separate incidents, with photographs of his injuries showing "extensive" bruising to the back of his legs.
Miss Forsyth said the boy had been left distressed by the experience.
He told police "Waqar would call him names like 'paedo'," in the classroom, Miss Forsyth added.
"He describes how this has had a great effect on him, causing him to lose hair as he was getting very stressed," she said.
"When he was bruised he would try and hide them with clothing even in very hot weather and make excuses not to go to the centre, such as having tummy ache."
Charanjit Jutla, defending, said both defendants were men of previous good character and deeply regretted their conduct.
Judge Mark Wall QC told them: "These were not assaults committed in ignorance of how inappropriate it was to use corporal punishment such as this."
He added: "Acts of brutality of this sort which you each indulged in, with a stick, will not be tolerated."
Two Islamic school teachers who beat a 10-year-old boy with a stick for reciting the Koran incorrectly have been jailed for a year.