The Swans qualified for continental competition through their Capital One Cup triumph over Bradford at Wembley, and Michael Laudrup's side have been rewarded with a pair of potentially tricky opponents.
If there is to be an all-British clash, Hibs will have to overcome a 2-0 first-leg deficit when they host Malmo in the return leg of their second qualifying round contest at Easter Road next Thursday.
Swansea will stage the first leg at their Liberty Stadium home on August 1, before making the trip to Scotland or Sweden the following week.
Swansea last tasted continental competition courtesy of their Welsh Cup success back in 1991.
But their Cup Winners' Cup campaign was ended in emphatic fashion as they lost 10-1 on aggregate to a star-studded Monaco side managed by Arsene Wenger and including George Weah and Youri Djorkaeff.
On this occasion Swansea will enter Europe under the English flag, having qualified as representatives of the Football Association, as opposed to the Football Association of Wales.
Should Hibs manage to overcome Malmo it would mean the Edinburgh club's new signing Owain Tudor Jones would come up against his former side.
Wales cap Jones enjoyed a four-year spell with the Swans between 2005 and 2009.
Source: PA
Source: PA