Subway said in a statement: "Like most Americans, and like Michael Phelps himself, we were disappointed in his behaviour. Also like most Americans, we accept his apology. Moving forward, he remains in our plans."
It is understood that Subway had a TV ad campaign featuring Phelps that was due to break imminently. However this has now been put on the back burner.
Subway's stance is different to Phelp's other sponsor Kellogg's. The cereal manufacturer said last week that it would not be renewing his contract after the News of the World published the picture of him smoking marijuana.
Kellogg's described his behaviour as "inconsistent with the company's image".
Phelps, who has apologised for using "bad judgement", also earned himself a three month suspension from USA swimming over the incident.
Other sponsors, including Speedo, Omega, Visa and Pure Sports, were quick to express support for the Olympic champion but Subway waited a week to give its verdict on his behaviour.
DMG Entertainment, the agency that brokered Phelps' lucrative ad deal with Mazda in China has said the company is standing by him although Mazda has not formally expressed a response to the incident.