The probe was initiated after the Los Angeles-based Drip Doctors clinic tweeted that it had treated Nasri.
"Following the publication of this information, the agency launched an investigation to find out what the treatment is," a source from the AEPSAD agency told AFP on condition of anonymity.
"The presence of a sportsman in a clinic like this is suspicious as such."
The probe was initiated after the Los Angeles-based Drip Doctors clinic tweeted that it had treated Nasri, saying its Immunity Drip IV would allow the French player to stay hydrated and on top form throughout the tough season.
Drip Doctors say they specialise in not only intravenous vitamin therapy and hydration, but also anti-aging and cosmetic enhancements.
The drip treatment Nasri allegedly received includes vitamins C and B, amino acid lysine and zinc, all combined with "specially formulated nutrients to help combat superbugs and common viruses".
The report went viral after Nasri's twitter account was hacked.
The Spanish Anti-Doping Agency was in contact with "all parties", the source said.