In all, 4,029 people from around Sweden are listed in the database. Over 1,000 of them are children. Many of those registered are not suspected of committing any crime.
The registry, marked "travelers", reportedly sits in a folder in the computer system of the Skåne police in southern Sweden.
Speaking to news agency TT, Ask said: "I'm shocked because I know we have laws and regulations when it comes to the police's ability to store personal information. You cannot store details about people just because of their origin."
"I have now demanded a proper investigation into what the facts are and in what way (the information) has been dealt with. As far as I understand the National Police Board hasn't known about this, but before we have all the facts on the table it's a little difficult to say exactly what has gone on."
Democracy Minister Birgitta Ohlsson added: "If this is true it is not only scary, unethical and unacceptable. It is of course also illegal."
“This is upsetting to say the least. Registration based on ethnicity is illegal and does not belong to a society governed by the rule of law,” said Minister of Integration Erik Ullenhag.
Meanwhile, National Police Board chief Bengt Svensson said the registration of thousands of Roma is completely unacceptable.
"As far as I can see there is no legal basis for this," he wrote in a press release, adding that the responsibility lies with the local police in Skåne.
"The police authorities in Skåne will file a report to the unit for internal investigation, which means the investigation will be led by a prosecutor," wrote Svensson.
There were strong reactions from within Sweden's Roma community on Monday.
Fred Taikon, publisher of the É Romani Glinda magazine, told news agency TT that he was dumbfounded after hearing the news:
"This is a terrible, unlawful action that the police are committing. It is forbidden to register people based on their ethnicity - and that is exactly what the authorities are doing."
Hans Caldaras, an artist and author of Roma origin, told Swedish Television News: “It is frightening and totally unacceptable that something like this can happen in Sweden."
Caldaras said that the registry brings to mind the early 1940s, when Swedish police, acting in response to the Nazis, mapped Roma and Jews living in Sweden.