The decision to put Archibald in temporary charge comes after McNamara was named Dundee United's new boss on Wednesday afternoon.
The former Celtic full-back was joined in the move to Tannadice by number two Simon Donnelly, with Partick sitting second in the Irn Bru First Division, five points behind leaders Morton but with two games in hand.
A statement released by the Glasgow club explained they were "bitterly disappointed" by the departure of their management duo but showered support on Archibald, who will be assisted by former team-mate Scott Paterson.
It said: "It is our belief that our current squad of talented young players are the best to have represented our club for many years.
"We are nicely placed in second position in the First Division and have a Ramsdens Cup Final to look forward to in April.
"We have every reason to look forward to both the remainder of this season, and beyond, with optimism, but it's important to retain continuity.
"With that in mind we would like to confirm the interim appointment of Alan Archibald as our manager.
"Working on a day-to-day basis with the players, Alan has played a pivotal role in our success so far this season and the directors feel that his interim appointment will offer the short-term continuity required."