Janne Andersson's side kick off their European Championship campaign against Spain in Seville on June 14 and also face Slovakia and Robert Lewandowski-led Poland in Group E.
They came out on top at the Friends Arena just outside Stockholm thanks to goals from Emil Forsberg, Marcus Danielson and Marcus Berg.
Forsberg opened the scoring in the 16th minute when his weak free-kick somehow squeezed past Armenia goalkeeper David Yurchenko.
RB Leipzig midfielder Forsberg then turned provider 11 minutes before the break when his free-kick was headed home via a deflection by Danielson.
Sebastian Larsson missed a penalty two minutes later and the away side pulled one back just after the hour mark through Vahan Bichakhchyan, who nodded home on the rebound after his shot was saved by Robin Olsen.
However Berg made sure of the win with five minutes left when he deftly finished past Yurchenko following a neat Robin Quaison pass.
After a much-touted return to the national team at the end of March following an almost five-year hiatus, Ibrahimovic had his sights set on once again playing in an international tournament.
But hopes of Ibrahimovic playing at the Euro were dashed in mid-May when his club AC Milan announced he had injured his left knee and would be out for at least six weeks.