Yasin Mahamoud, 23, was convicted of trying to lure the victim to a music studio in Stockholm in March last year.
The plot failed but the victim was kidnapped, beaten and robbed several weeks later without Yasin's involvement.
The rapper denied the charges and his lawyer told local media he will appeal against the verdict.
Mahamoud - who is known just as Yasin in the music world - was jailed on Wednesday as part of a broader case involving a large criminal network accused of various crimes in the Swedish capital last year.
Some 27 people were convicted of serious crimes, including attempted murder, robbery and extortion, and imprisoned for a combined total of 147 years.
The leader of the network, Chihab Lamouri, 33, received the longest sentence of 17 years and 10 months in prison.
Prosecutors said the kidnapping was aborted, but a second plot involving another prominent Swedish rapper, Haval Khalil, was carried out weeks later in April.
Khalil told the victim to come to a flat, where he was blackmailed after being tied up, attacked and photographed in humiliating circumstances, prosecutors said.
A rising hip-hop star from Stockholm, Yasin has released two chart-topping albums in Sweden since breaking through as a recording artist in the mid-2010s.
In March this year, Yasin was named Artist of the Year and Hip-Hop/RnB Artist of the Year at Sweden's prestigious P3 Gold awards.
The rapper could not collect the award in person because he was in custody at the time in connection with the kidnapping.
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