Ricciardo had surgery in Spain on Sunday after breaking his left hand in a crash in practice at the Dutch Grand Prix on Friday, with reserve driver Lawson drafted in for his Formula One race debut.
The next race, round 14, is the Italian Grand Prix at Monza on Sunday.
Singapore follows on September 17th and Japan on September 24th.
"We are delighted that Daniel’s surgery went well and that he is now on the road to recovery," AlphaTauri said in a statement.
"We hope to see him at the track again very soon, but until he is fully fit, we can confirm that Liam, who did a good job in difficult circumstances in Zandvoort, will continue to drive alongside Yuki (Tsunoda), starting from our home race this weekend in Monza."
Lawson finished 13th in the Dutch Grand Prix, with Tsunoda 16th.
