After a six-hour hearing, a disciplinary panel found the 29-year-old bit Waller on the arm during Saracens' 27-12 Premiership victory at Allianz Park on Saturday.
The panel looked at two counts of biting but dismissed the second charge.
Ashton, who denied both offences, can play again on 19 December.
Philip Evans QC, who chaired the disciplinary panel, said: "Having considered detailed evidence, the panel concluded that during the course of a ruck Chris Ashton bit the arm of Alex Waller at a time that Mr Waller was attempting to clear him out."
The minimum suspension for a guilty verdict was 12 weeks, with a more serious offence potentially carrying a punishment of up to 208 weeks.
Evans said Ashton's offence was at the lower end of the scale but "aggravated by his previous record".
Ashton was banned for 10 weeks last season for gouging.
The ban puts a further dent in his hopes of resurrecting his England career.
Ashton has been capped 39 times and was in Eddie Jones' Six Nations squad this year.
However, he was ruled out of the tournament after failing to overturn the 10-week ban for making contact with the eyes of Ulster's Luke Marshall in a European Champions Cup match.
He was then left out of the squad which toured Australia in the summer.
His last England cap came in the summer of 2014, against New Zealand.
