Strictly speaking, no. That would mean "little brush." The suffix "-ino" is a diminutive that makes whatever it is attached to smaller. It would be understandable that you are talking about a brush, but, if there are multiple brushes that you could be talking about (for example, a hairbrush and a toothbrush), the listener might confuse which one you mean to discuss.
This link provides more info: https://www.thoughtco.com/alteration-in-italian-diminutives-2011565