Youngs was cited following the incident in Tigers' 41-32 Aviva Premiership win at the Madejski Stadium on March 25, and his club suspended him for one week after an internal hearing.
That saw him miss Friday's win over Worcester, but his RFU ban will run alongside his Leicester suspension, meaning he will be free to play from Thursday and is available for the remainder of the Tigers' title run-in.
An RFU statement said: "Ben Youngs of Leicester Tigers was this afternoon suspended for one week after pleading guilty to striking London Irish's Jamie Gibson with his knee, contrary to Law 10(4)(a), during the Aviva Premiership match at the Madejski Stadium on March 25."
The hearing was chaired by Judge Jeff Blackett, and the RFU's disciplinary chief praised Leicester for their "responsible" handling of the incident.
The low-end entry point for striking with the knee is a three-week ban, but Blackett revealed that Youngs' good disciplinary record and the mitigating factor that he was being held down by Gibson in the lead-up to the incident had seen his potential suspension reduced.
Blackett said: "We decided that the offence was at the low end of seriousness, which carries an entry point of three weeks.
"There were no aggravating features and on the basis of his good record this was reduced by 50%.
"Taking into account RFU Regulation 19.11.13 there was a compelling mitigating factor in that the player was being held down unlawfully for a substantial period and so we reduced the suspension further to one week.
"We would like to thank Leicester for their responsible attitude towards this case."
A lengthy ban could have put Youngs in danger of missing England's summer tour to South Africa, but he will be available for selection when new full-time head coach Stuart Lancaster chooses his squad to face the Springboks.
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