Tinnitus is the chronic perception of a phantom sound with different levels of related distress. Past research has elucidated interactions of tinnitus distress with audiological, affective and further clinical variables. The influence of tinnitus distress on cognition is underinvestigated. Our study aims at investigating specific influences of tinnitus distress and further associated predictors on cognition in a cohort of n = 146 out-ward clinical tinnitus patients. Age, educational level, hearing loss, Tinnitus Questionnaire (TQ) score, tinnitus duration, speech in noise (SIN), stress, anxiety and depression, and psychological well-being were included as predictors of a machine learning regression approach (elastic net) in three models with scores of a multiple choice vocabulary test (MWT-B), or two trail-making tests (TMT-A and TMT-B), as dependent variables. TQ scores predicted lower MWT-B scores and higher TMT-B test completion time. Stress, emotional, and psychological variables were not found to be relevant predictors in all models with the exception of small positive influences of SIN and depression on TMT-B. Effect sizes were small to medium for all models and predictors. Results are indicative of specific influence of tinnitus distress on cognitive performance, especially on general or crystallized intelligence and executive functions. More research is needed at the delicate intersection of tinnitus distress and cognitive skills needed in daily functioning.