“It was just luck” that the device did not explode and nobody was harmed, in the early morning attack, in the town of Villingen-Schwenningen, regional police spokesman, Thomas Kalmbach, said.
Forty percent of Germans want Chancellor Angela Merkel to resign over her refugee policy.
The country took in 1.1m asylum seekers last year and there have been multiple attacks, although most of them have been incidents of arson involving unoccupied buildings.
Justice minister Heiko Maass said the grenade attack represented a new level of “hate and violence” and that he was summoning his state counterparts to better co-ordinate local and federal measures to prevent and prosecute anti-immigrant hate crimes.
“Grenades are already flying towards refugee homes; we can’t wait until there is someone dead,” he said.
“We need to do everything we can to ensure xenophobic crimes are more rapidly solved and punished more severely.”
Police formed a special task force to look for the culprits who threw the grenade towards the home at 1.15am, Mr Kalmbach said.
The grenade still contained its explosives.
A bomb squad destroyed the device on the scene at 5am, after evacuating the 20 residents from the home.
Merkel, who enjoyed record high popularity ratings early last year, has grown increasingly isolated in recent months.
Her conservative bloc has pressed her to take a tougher line on asylum seekers and European allies have dragged their feet on the issue.
Responding to popular pressure, Merkel’s conservatives, and their left-leaning Social Democrat (SPD) coalition partners, agreed on Thursday to tighten asylum rules, compromising on how to stem the influx.
The Insa poll, for Focus magazine, surveyed 2,047 Germans between January 22 and January 25.
It showed 45.2% believed Merkel’s refugee policy was not a reason for her to resign. It was the first time the pollster had asked voters whether Merkel should quit.
Another poll, released yesterday by the Elector Research Group, showed support for Merkel’s conservative bloc steady, at 37%.
As recently as September, they were on 42%. Support for the SPD was also unchanged, at 24%.
The poll put the right-wing Alternative for Germany (AfD), which supports a hard line on immigration, on 11%.
The three ruling parties — Merkel’s Christian Democrats, their Bavarian allies, and the SPD — are eager to show voters that the government is in control of the refugee crisis, before three state votes in March and a general election next year.
A dispute over tighter immigration rules has, nonetheless, strained the ruling coalition.