Police suspect arson in both cases, which caused no injuries. No arrests have been made.
“Everyone got out of the building. There were nine residents and two staff members who got themselves out,” Johan Winsnes from the Stockholm emergency services centre told news agency TT.
The nine asylum seekers living of the centre in the well-heeled northern suburb of Sigtuna and two staff members were evacuated before firefighters arrived shortly before 2 am.
Around 20 firefighters tackled the blaze, but the building could not be saved.
A previous fire hit a home in Stockholm's working-class Fagersjö neighbourhood early on Sunday. All 40 residents were evacuated safely.
Sweden accepted the second highest number of refugees per capita in the European Union in 2015, receiving a record 163,000 asylum applications, as the continent struggles with its worst migration crisis since World War II.
The nation saw a wave of around 20 arson attacks against refugee centres last year, but the culprits have rarely been caught.