Said cleaning utensil includes a bottle brush (2) having a gripping handle (4) that is combined with a bottle-cleaning head (5), the gripping handle (4) including a storage cavity (7) wherein is removably inserted a nipple brush (3), including a gripping handle (9) and a nipple-cleaning head (10) that has radially positioned, substantially straight fibers. Additionally, the storage cavity (7) has a transverse cross-section having a large axis and a small axis, and the cleaning head of the nipple brush (3) has, in the transverse cross-section thereof, a maximum size substantially equal to the large axis of the storage cavity (7) such that the fibers of the portion of the nipple-cleaning head (10) that are positioned in the storage cavity at the large axis remain straight.