While none of the attacks are related, at least two appear to have been carried out by asylum seekers.
Sunday's bombing, which killed only the attacker but injured 15 others, was carried out by a 27-year-old Syrian national in the southern city of Ansbach. The attacker's application for asylum had been rejected but he was able to stay in the country anyway.
Just hours before, another 21-year-old Syrian asylum seeker killed a woman
in Reutlingen, attacking her with a slicing knife nearly two feet in length.
The country was already reeling from a shooting spree
in Munich on Friday by an 18-year-old German-Iranian that left nine people dead. That attacker was not an asylum seeker -- he was born and raised in Munich.
And last Monday, a 17-year-old carried out an ax attack
on board a train outside of Wurzburg. He was originally reported to be an Afghan refugee, but his nationality and refugee status have since come into question.
As Germany grapples with an extraordinary week of violence, critics have raised concerns over the system for admitting and settling asylum seekers and migrants from war-ravaged countries.
Here are some questions answered about how the system works:
Who can stay?
Sunday's suicide bomber entered Germany two years ago and his application for asylum had been rejected, according to authorities.
But he was able to remain in the country, as rejected applicants cannot legally be deported to a place where they face serious harm -- Syria's war zone is clearly one of them.
This leaves the bomber, and many more asylum seekers like him, in a state of limbo
, unable to gain residential status or return to their homeland.
"While they wait for an appeal to go through or a change in their circumstances, they're also not permitted to work or receive benefits," explained CNN's Tim Lister, who estimated that tens of thousands of migrants in Germany were in this position.
How does it work?
On entering Germany, refugees are placed in a reception center, where a long procedure for asylum
While applications are being considered by the Federal Office for Migration and Refugees (BAMF), asylum seekers are given temporary rights to stay while their case is heard.
"If neither asylum nor refugee protection is granted, the BAMF examines whether there are grounds for a deportation ban -- this can be an extensive review," said Lister.
Meanwhile, those granted asylum status receive a temporary residence permit and are given the same status as Germans within the social insurance system -- meaning they are entitled to social welfare, child benefits, integration allowances and language courses.
Many of these attacks, including the Munich shootings, happened in or near the southeastern German state of Bavaria, which is the first point of contact in the country for many Middle Eastern migrants arriving through Greece and then the Balkans.
"The Munich residents were really the ones in Bavaria who came out with big placards saying 'welcome refugees' -- there was a huge movement to accept refugees at the time," explained CNN's Berlin-based correspondent Atika Shubert.
"I think that probably now a lot of people might be starting to think: 'Well, we welcomed a lot of refugees, but is this now coming back to harm us?'"
Since the initial influx of refugees, there has been a concerted effort by the German government to spread them beyond Bavaria to hostels and camps across the country.
What does the public think?
During a memorial for the victims of the Munich shooting over the weekend, Shubert found a number of people questioning whether the recent string of attacks was due to an increase in refugee numbers.
"Even though these attacks are unrelated -- and one was carried out by a German-born national -- the public in part see it as a wider threat brought about by the influx of refugees," said Shubert.
"On a normal day, this is not how people feel," she continued. "But because you've got some of these attacks perpetrated by refugees, it's playing into their worst fears."
Against this backdrop, the far-right political group Patriotic Europeans Against the Islamisation of the West -- known as Pegida -- will also be capitalizing on any resentment of foreigners.
What does this mean for Merkel?
Chancellor Angela Merkel's plan to set aside 6 billion euros ($6.8 billion) to house and care for 800,000 new refugee
applicants last year is coming under greater scrutiny from the public.
"When the refugee crisis initially started, people were already skeptical that the government had the ability to actually handle the sheer numbers that were arriving," said Shubert.
"So when you see these violent attacks, it compounds this feeling that Merkel may have had good intentions by opening the door, but that there was no plan to adequately deal with the influx."