The proposed measure would allow the federal criminal police to electronically track the movements of a person deemed a security threat, even before they have been convicted of a crime.
"Ankle bracelets are not a panacea but they are an important instrument to facilitate the surveillance of dangerous people," Interior Minister Thomas de Maiziere said after the cabinet agreed to a change in the law to allow the measure.
The proposal still has to be approved by parliament.
It comes as part of a series of security reforms announced in response to the December 19th attack in which Tunisian national Anis Amri ploughed a truck into a crowded Christmas market in Berlin, killing 12 people.
The attack was claimed by the extremist Isis terror group, with Amri shot dead by Italian police in Milan several days later.
Public anger quickly erupted after it emerged that Amri was already on the radar of intelligence services and was known to have links to Islamist radicals.
As a failed asylum seeker, he should have been deported months before the attack but Tunisia failed to send the necessary paperwork in time.
The German government has since vowed to speed up deportations and mooted plans to place rejected asylum seekers who are considered a threat in detention ahead of their expulsion.
German security services have a list of more than 550 Islamists considered "threats to public security" who have lived or currently reside in Germany.
Interior ministry spokesman Johannes Dimroth declined to speculate how many suspects might now face electronic monitoring.
"How many of them could in the future be affected by such a measure is a purely hypothetical question," he told reporters in Berlin.