They were not called MAZ, but there have been some sportscars privately built by MAZ employees in the factory's sports club. Of course, those were not factory projects, but they gave birth to this car, so I'd count them in. Actually, I'd consider them predecessors of the 1500.
Here is Yuri Kolobov from MAZ during the event at Neva Ring in 1960 (from ZR magazine). You can note the logo on the car, which refers to the 'Red Flag' sporting society from Minsk. He raced in 1600cc class, with another car being entered by Vladimir Maiboroda, who was the designer of MAZ 1500. Another MAZ employee, P.Timofeev, drove in 3000cc category in 1960.