Icardi has become crucial to the Nerazzurri since joining from Sampdoria in 2013, scoring 122 goals in 210 outings while lifting the Capocanniere award for Serie A's most prolific scorer on two occasions.
But that record has not always translated into a glowing relationship between the striker and his club, with directors and fans alike at times exasperated by the behaviour of Icardi and wife and agent Wanda Nara.
One particular bugbear has been Icardi and Nara's apparent sustained courtship of Real Madrid, with the Argentine a regular visitor to the Spanish capital and a guest at the Bernabeu for December's Copa Libertadores final between Boca Juniors and River Plate.
And Inter will have to do without their star on Thursday after Spalletti confirmed his absence in the wake of their earlier revelation that Samir Handanovic would be taking over captaincy duties.
"Icardi was called up, and has decided not to travel to Vienna," the coach explained to Sky Sport.
"Tomorrow we have a big game, there will be time to clarify things. It has been a tough, painful decision which he probably has not taken well, made with the team's well-being in mind.
"The things going on around Icardi have disturbed us, both him and the team which he used to captain. But we think it is for the best on the pitch, from the next game onwards. We hope that the players react properly."
Icardi's future at San Siro remains shrouded in doubt, with little progress made on a contract extension that the club is keen to push through in order to scare off interest from the likes of Madrid.
Agent Wanda explained that her husband's priority was Inter, but insisted that there was "no rush" to sign.
"There has been a lot of nonsense said about Mauro, for example a supposed fine that did not exist," she said in recent comments to reporters.
"I would like Mauro to be more protected by the team. I cannot understand if these bad things come from outside or within."
Nara also criticised Spalletti, whom she sees as responsible for Icardi's spluttering form in front of goal this season - the Argentine has netted just nine so far, half of the number managed by current Serie A top scorer Cristiano Ronaldo.
"Why is Icardi not scoring. He has always scored," she fired after Saturday's 1-0 victory over Parma, with the single goal coming from substitute Lautaro Martinez.
"Lautaro netted thanks to some great movement by Mauro, who was rarely accompanied. Maybe Spalletti should have put Lautaro in earlier.
"He is taking advantage of the fact that Mauro and Lautaro are friends and that there is no rivalry between them."