The Kazakh-funded team of Tour de France winner Vincenzo Nibali provisionally suspended Iglinskiy after the International Cycling Union (UCI) ruled late on Wednesday that the Kazakh had failed an EPO test on 1 August.
"In accordance with regulations of the MPCC (Movement for Credible Cycling) to which the Astana team first adhered in 2013, the rider is suspended provisionally and shall remain out of competition in anticipation of the results from the B analysis," Astana team manager Alexandre Vinokourov said in a statement.
"All Astana Pro Team riders are contractually obliged to respect strict ethical rules and regulations."
MPCC regulations, however, also state that a team must suspend themselves from racing for eight days in the case of multiple positive tests in the past 12 months.
Iglinskiy's brother and team-mate Valentin was also suspended last month for failing an EPO test in August.
Self suspension begins on the first day of the next World Tour race, meaning Astana are set to miss next week's Tour of Beijing, the final race of the UCI World Tour.
Astana officials were flying to Almaty on Thursday and were unable to comment.
The MPCC reminded Astana of their obligations should Iglinskiy's B sample also be positive.
"In this case, according to the MPCC regulation, a member team agrees on a voluntary basis to temporarily suspend operations for eight days from the next World Tour race," it said in a statement.
"This approach does, however, apply only after the result of the counter-analysis, if the rider requests it. MPCC has specifically asked the Astana team to hear its rider Maxim Iglinskiy, in order to know if he makes a confession or requests counter-analysis.
"If this counter-analysis is claimed, MPCC wishes that the result will be quickly released, as it was already the case in similar circumstances last year."
In June last year, French team AG2R-La Mondiale sat out of the Dauphine, a prestigious one-week race ahead of the Tour de France, after two of their riders had failed dope tests.