Kubista began his academic career in 1991 as an Assistant Professor in the Department of Physical Chemistry at Chalmers University of Technology. From 1993 to 1997, he served as an Associate Professor in the Department of Biochemistry at the same institution. Following this, he held the position of Professor in the Department of Biochemistry at Chalmers University of Technology from 1997 to 2006. Since 2007, he is the Head of the Department of Gene Expression at the Institute of Biotechnology, BIOCEV, Czech Academy of Sciences.