The investigations involve instances where voters on Facebook were offered 300 kronor to "vote the right way for Sweden."
The post has circulated in buy-and-sell groups under the heading "Votes wanted," according to the newspaper.
The post has been reported to the Swedish Election Authority.
"A preliminary investigation is underway regarding the offence of exerting undue influence on voting," Maria Fredriksson, press spokesperson for the Police Region North, told Piteå-Tidningen.
"There are two cases. One concerns a buy-and-sell page in Luleå and the other one in Piteå. However, they involve the same post," she said.
No political party is named in the post. However, it includes a call not to "vote red," and the accompanying image is taken from the cover art for a campaign song by high-ranking Sweden Democrat politician Björn Söder.
The image depicts a car featuring a Sweden Democrat brand bumblebee.
"Buying votes is something one shouldn't engage in. I condemn it," said Magnus Häggblad, the Sweden Democrats' district chairman in Norrbotten, to the newspaper.
Newspaper Dagens Nyheter (DN) also reports that a new preliminary investigation into suspected electoral fraud—specifically, improper influence on voting—is underway.
The case was referred to the National Anti-Corruption Unit on Wednesday; it remains unclear where the alleged crime took place and whether it concerns the same matter as the cases in Piteå and Luleå or something else entirely.
"I haven't had time to look at it yet," prosecutor Oskar Edvardsson told DN.