Phelan, whose contract had been due to end in December, brought forward his decision to leave after his team finished bottom of the southern hemisphere Rugby Championship for the second year in succession with six defeats.
"Santiago Phelan will not continue his job as head coach of the Pumas after six years in charge," the UAR said on its website.
"The national team's head coach communicated his decision to the UAR's executive board and he will not lead the team during the tour in November of England, Wales and Italy."
The UAR, who would ideally like to appoint a foreign coach as Phelan's successor, is expected to announce a stand-in for the tour at a news conference on Tuesday.
'Tati' Phelan, a former Pumas flanker, took the post when his predecessor Marcelo Loffreda quit after steering them to third place at the 2007 World Cup in France.
He led Argentina into the quarter-finals of the 2011 World Cup in New Zealand but otherwise had a tough time retaining the high standard the Pumas had reached under the captaincy of former scrum-half Agustin Pichot.
Phelan's record in 45 matches as coach included 13 wins, 31 defeats and a draw against South Africa in last year's debut Rugby Championship.
He began his tenure with a Test against Scotland in Rosario in June 2008 and ended it at the same venue with this month's crushing 54-17 defeat by Australia in their last Rugby Championship match.
Local media said Phelan, who had said earlier in the season he was considering quitting at the end of the year, had lost some grip on his squad and that there were also rifts in his coaching staff.
The Pumas open their European tour with a demanding Test against England at Twickenham on November 9. They meet Wales in Cardiff and Italy in Turin on the following two Saturdays.
England beat Argentina 2-0 in a two Test series in Salta and Buenos Aires in June when both fielded largely second string teams.