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."

Leeds, playing under head coach Thomas Christiansen for the first time, went ahead through Phillips' smart finish.
Last season's top scorer Chris Wood then headed in for 2-0, only for Bolton forward Gary Madine to nod home.
But Phillips' tap-in quickly restored Leeds' two-goal lead, and they held on despite Adam Le Fondre's penalty.
The former Reading front man smashed his spot-kick down the middle, with Conor Shaughnessy having fouled Madine almost immediately after coming on.
But the headlines belonged to 21-year-old Phillips, who doubled his career tally for Leeds during the first half to put the visitors in control.
New Zealand forward Wood, who scored 30 goals last season as Leeds narrowly missed out on the play-offs, also opened his account with a clinical header in off the underside of the bar.
But there will be some concern over the fitness of defenders Gaetano Berardi and Matthew Pennington, who were both forced off injured prior to half-time.
Bolton, promoted from League One in May, were direct throughout but struggled to create anything clear-cut from open play - and also lost midfielder Josh Vela through injury at the end of the game.
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.
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Kalvin Phillips scored twice as Leeds United opened their 2017-18 Championship campaign with victory at Bolton Wanderers.