"Two persons have been arrested in Gothenburg on probable cause on suspicion of terrorist crimes in committing murder," the Swedish Prosecution Authority (SPA) said in a statement.
The arrests were made in cooperation with the Swedish Security Police, according to the authority.
The SPA also said that an arrest warrant was issued for a third suspect.
However, the SPA said it could not provide further information regarding the case due to the sensitivity of the investigation.
"The investigation is at a very sensitive state. We will undertake intense investigation work, and more information and details of the crime will come during the proceedings," security police spokesperson Sirpa Franzen told the Swedish news agency TT.
TT also reported that Interior Minister Anders Ygeman found the arrests "very encouraging." Ygeman added that the case was first time people suspected of traveling abroad to commit terrorism would be tried by Swedish courts.
Around 300 Swedes have travelled to Syria and Iraq to fight with militant groups - including the so-called "Islamic State" and al-Qaeda - the head of Sweden's security police told Reuters news agency in March.The chief of security police added that around 35 had been killed in fighting, while 80 had returned to Sweden.