Mohammed Siddique, 60, and his son Mohammed Waqar, 24, both teachers at the Birmingham Islamic Centre, admitted wilful cruelty to a child under 16 in the court.
The child was attacked on four separate occasions at the Jamia Mosque at Sparkbrook in Birmingham, between May and June 2014, Birmingham Crown Court heard.
Besides the prison sentence, the pair also face a teaching ban.
Prosecutor Sam Forsyth told the court that 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".
"He describes how this has had a great effect on him, causing him to lose hair as he was getting very stressed," she said.
Defence lawyer Charanjit Jutla said both defendants were men of previous good character and "deeply regretted their conduct".
Judge Mark Wall told them: "These were not assaults committed in ignorance of how inappropriate it was to use corporal punishment such as this.
"The use of a weapon to hit a 10-year-old child, as you both well know, is wholly unacceptable in this day and age. There must be no mistake about the message that should be taken from this case.
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