Robinson visited with team doctors at the Commanders' facility Tuesday, Washington coach Ron Rivera said.
Washington kept Robinson on the 53-man roster, but he'll continue to be examined by doctors over the next few days.
As the Commanders learn more about his recovery -- and possible timeline for his return -- they will determine whether he'll stay on the active roster or be placed on the non-football injury list. If he's placed on the latter, Robinson would miss four games.
Rivera said Robinson did not suffer structural damage from the gunshot wound. That would help his recovery, but there's still no certainty about when he'd return.
"They have no timeline now," Rivera said Tuesday. "It's a very fortunate and unique situation and as we go through it we'll know what the timeline will be."
Robinson was shot in Washington, D.C., early Sunday evening. He underwent surgery and posted an Instagram story that his "surgery went well."
Depending on what doctors determine Tuesday, Robinson could be placed on the non-football injury list, which would require him to miss the first four games.
On Monday, Rivera said the doctors were positive about his situation.
"He's very fortunate," Rivera said. "He's doing well. It will be a matter of time before he's back out here. There's no timeline, but everything was very positive.
"It's just about the healing process, and once he's well enough to get on the field, doctors have to clear him and we'll go from there. Everything is positive so far."
Robinson, a third-round pick in April, had emerged as Washington's primary running back on early downs because of his consistency and power running between the tackles. The Commanders still have veterans Antonio Gibson, who rushed for 1,037 yards last season, and J.D. McKissic, their third-down back who has 123 catches in 27 games with Washington the past two years.
Gibson can help in the pass game as well. The Commanders also have versatile receiver Curtis Samuel, who can occasionally line up at running back in certain packages. But if Robinson is going to miss multiple games, they'll have to keep another running back on the 53-man roster.
Robinson was shot twice in the lower body in an armed robbery attempt. Robinson had gone into the District of Columbia to get something to eat. The incident happened shortly before 6 p.m. ET in the 1000 block of H Street Northeast.
When police arrived on the scene, they located Robinson, who was suffering from "a couple gunshot wounds to his lower extremities," according to Dustin Sternbeck, director of communications for the Metro Police Department in Washington. Robinson was treated by paramedics at the scene and transported immediately to a hospital. One bullet hit his glute and another struck him in a lower leg.
Sternbeck said police have identified two potential suspects and recovered a firearm a short distance from where the shooting occurred. According to the police report, the incident was described as aggravated assault.
According to the report, Robinson wrestled away a handgun from one assailant but was shot by the other, who also was using a handgun. Both suspects are believed to be teenagers; the Metro Police Department released photos of the alleged suspects on its Twitter feed Monday night. The investigation remains ongoing.