Mathis said in a statement released through his official Twitter account that his failed test was a result of fertility drugs which his doctor said would not violate the NFL's policy on performance-enhancing substances.
"I made the mistake of not calling the NFL or NFLPA to double check before I took the medication at the end of last season," said the 33-year-old, whose wife had twins in 2012 and is expecting another baby this year.
"The union has worked very closely with me to present all of the facts and medical records for consideration of discipline that does not include a suspension because of the unique facts of my case, but the Commissioner refused the request."
The six-time Pro Bowl selection will be eligible to return to the Colts' active roster on Sept. 29 after the team's Week 4 game against the Tennessee Titans.
In a statement, the Colts said: "We recognize the extreme seriousness of this matter and will honor the confidentiality requirements of the league's program.
"We nevertheless wish to assure Robert and our fans that he remains an honored and cherished member of the Colts family and that we support him as he deals with this difficult challenge."
Mathis, one of the most respected leaders for the Colts, led the league with a franchise record 19.5 sacks last season.