Alvarez, the reigning American League Rookie of the Year, and Urquidy, the team's presumed No. 4 starter at spring training, did not reported to summer camp July 3.
Both were later placed on the injured list, and neither made the team's 30-man Opening Day roster.
They are now expected to report to the Astros' alternate site in Corpus Christi, along with the other players who are injured or did not make the 30-man roster.
Manager Dusty Baker said Friday during a conference call he has no idea how long it will take either player to get ready for the season.
Neither of them have been able to participate in baseball activities on their own while absent over the past few weeks, Baker said.
"It kind of varies per person," Baker said. "I know they'll probably say they're ready sooner than they are. No matter what they tell me, I'd probably still give them another couple of days because I know how players are anxious to get back. They missed a lot of time. It's going to take probably almost equal time that they've missed to get back.
"So, we'll be in constant contact with the people down in Corpus and we're relying on their opinion on them and their progress."
Kyle Tucker and Aledmys Diaz are expected to fill Alvarez's role as DH until he's ready to play.
Urquidy's No. 4 spot in the pitching rotation went to Josh James, and the No. 5 starter to begin the season is Framber Valdez.
Also returning to baseball activities are left-handed pitcher Cionel Perez and right-handed pitchers Shawn Dubin and Ralph Garza Jr.