This follows after the club suffered a 3-0 humiliating defeat to regional rivals Great Olympics in the Ghana Premier League last Friday.
The Bosnian trainer took over the club last term and went ahead to play 17 games competitively.
Barjaktarevic managed only three wins during this period.
Cities opened the 2020/2021 campaign with a 1-1 draw against Berekum Chelsea at home a fortnight ago.
The Royals made about 14 new signings during the transfer window including the capture of Ghana legend Asamoah Gyan.
A new coach will be announced in the coming days.
Cities have been linked with moves for Eleven Wonders coach Ignatius Osei-Fosu, former Hearts of Oak trainer Kim Grant and ex-Ghana international Ibrahim Tanko.
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