The anti-migrant Alternative for Germany party (AfD) blamed the crime on the "uncontrolled" influx of foreigners, while the head of a police union warned of the "dangers that always go along with massive immigration".
But Vice Chancellor Sigmar Gabriel said the murder of the 19-year-old medical student should not be used to whip up hatred against all refugees.
"Such horrible murders already happened before the first Afghan or Syrian refugee arrived here," Gabriel told the Bild newspaper. "We will not allow incitement after such violent crimes, no matter who commits them."
The 17-year-old suspect, who arrived in Germany in 2015 as an unaccompanied minor, was arrested in the southwestern town of Freiburg on Friday after his DNA was found at the crime scene and he was identified on CCTV.
The victim was found dead on a river bank on October 16th. An autopsy found that she had drowned.
News of the arrest triggered strong reaction on social media with some people saying an ironic "thank you" to Chancellor Angela Merkel, whose open-door asylum policy brought a record number of migrants and refugees into Germany last year.
'Warnings written off'
The chairman of the DPoIG police union, Rainer Wendt, said the killing could have been prevented.
"We wouldn't have this victim, and so many others, if our country had been better prepared for the dangers that always go along with massive immigration," he told Bild.
His comments were slammed by Social Democrat (SPD) deputy chair Ralf Stegner, who wrote on Twitter:
“The statement by DPolG boss Wendt about the horrible act of violence in Freiburg is politically repulsive and dumber than what police should allow."
But others still echoed Vice Chancellor Gabriel, pointing out that violent crimes are committed by all types of people.
"Such brutality is unfortunately perpetuated by natives and foreigners. This unfortunately is not a new phenomenon," said CDU politician Julia Klöckner to Bild.
Conservative CSU internal affairs expert Stephan Mayer emphasized that immgirants and refugees should not all be painted as suspects.
Germany received 890,000 asylum requests in 2015, although that rate slowed to 213,000 from January to September 2016 following a deal with Turkey and a series of border closures on the Balkan route.
Public anger about the refugee arrivals has been stoked by some high-profile crimes involving immigrants.
During the last New Year's Eve celebrations, hundreds of women reported sexual assaults in Cologne and other German cities, with the attacks blamed largely on Arab and North African men.