Stars coach Seloatse Mosala made four changes to his starting line-up from their 1-0 defeat to SuperSport United in their previous Absa Premiership match.
It was Mukura who showed early intent as striker Frodouard Twizerimana was trapped off-side as the visitors looked to get an early goal away from home.
Tshepo Tema found himself in space and had a go from range but his effort went wide of the mark.
The first attempt on target came in the ninth minute as Gael Dhayindavyi looked to catch Badra Ali Sangare out with a shot from outside the box but the Stars keeper was untroubled.
Mukura had a glorious chance to go ahead after 15 minutes, but Twizerimana, after brilliantly rounding Sangare, could only find the side-netting with the goal at his mercy.
Just before the break, the hosts almost stole the lead as Omar Rwabugiri’s attempted punch ricocheted off his own defender and back towards goal, but Iddy Saidi was on hand to clear off the line.
Mukura coach Francis Haringingo had seen enough before half-time and made his first substitution in the 43rd minute, introducing a second striker Jean Iradukunda for midfielder Innocent Nizeye.
Stars controlled proceedings for much of the second half as the altitude looked to have affected the Rwandans, but failed to capitalise on their increased possession.
The likes of Yusuf Jappie and Sinethemba Jantjie sprung to life as they combined well up front but were both let down by wayward finishing in and around the 18-yard area.
Mosala then threw on Sthembiso Dlamini in place of Relebogile Mokhuoane at the hour-mark, and the new man made his introduction felt as he combined well to set up Harris Tchilimbou, whose shot from inside the box was blocked.
Jantjie carved out a chance for himself six minutes later, losing his marker with a superb turn at the edge of the box, but his right-footed shot sailed beyond the far post.
Sibusiso Hlubi and Judas Moseamedia later replaced Jappie and Eleazar Rodgers respectively, as Stars threw numbers forward in search of an advantage ahead of the away leg next week.
However, the finishing continued to leave plenty to be desired as the two sides settled for a goalless stalemate.
FS Stars: Sangare, Mbhele, Mahamutsa, Tema, Phungwayo, Makhaula, Mokhuoane (Dlamini 61'), Tchilimbou, Jappie (Hlubi 72'), Jantjies, Rodgers (Moseamedi 78')
Makura VS: Rugirayabo, Mutijima, Iragire, Nshimirimana, Nkomezi, Duhayindavyi, Ciza (Ndayishimiye 66'), Ndizeye (Iradukunda 43'), Twizerimana (Romami 70'), Issy Saidi.