Quinn's agent Sean Kiernan announced the suspension Thursday on Twitter.
"I am extremely disappointed in the NFL for following through with the suspension," Kiernan wrote in a statement. "In life there are real world instances where a totality of the circumstances must be analyzed. This is one such case."
Kiernan said Quinn has a medical history of seizures, requiring him to take multiple doses of preventative medication daily to regulate the seizures. Kiernan said Quinn was tested April 2 under the NFL steroid policy. He failed the test for a substance called probenecid. Probenecid is classified as a masking agent under the NFL's policy.
"He does not take any supplements and took nothing else during this period that would create a positive test for probenecid, in fact, he had no idea what probenecid was or what it was used for," Kiernan wrote.
Kiernan also said his party's "belief" is that Kiernan's seizure medicine became "contaminated" with probenecid.
Quinn, 29, joined the Cowboys in a March trade from the Miami Dolphins. The two-time Pro Bowl selection and 2013 All-Pro had 38 tackles, nine tackles for a loss, 6.5 sacks and two forced fumbles in 16 starts last season for the Dolphins. Quinn led the NFL with 23 tackles for a loss during his All-Pro campaign.
Cowboys coach Jason Garrett told reporters Thursday that the team stands behind the pass-rusher.
"We support Robert Quinn. We trust Robert Quinn," Garrett said. "We really like everything he's done for our team since he's been here. We're excited about his future with our team."
Quinn also sustained a broken left hand Tuesday at practice. The No. 14 overall pick in the 2011 NFL Draft played his first seven seasons with the Los Angeles Rams. The Rams traded Quinn to the Dolphins in March 2018.
Quinn is eligible to return to the Cowboys' lineup Sept. 15, following Dallas' game against the Washington Redskins.