According to design website Apartment Therapy, some professional upholsterers won't bother with small repairs, such as rips or tears in upholstery fabric. They likely won't have a match for the fabric and they can't ask much for their efforts, anyway, because it's a small repair. If you have found a rip in your upholstered furniture piece's fabric, you can repair the damage. You can close the tear and minimise its appearance using heat activated hem tape.
Measure your tear. Cut out a piece from your fabric that is 2 inches longer than your tear measurements and about 2 inches wider.
Insert your fabric piece into the tear, being careful to not expand the tear. Situate the fabric so it rests completely centred beneath the tear.
Cut a length of fusible hem tape. It shouldn't be sticky yet because its fabric adhesive surface is activated by heat. The hem tape's lack of stickiness will make it easy to insert the tape into the tear. Make your tape a little more than twice as long as your rip. Cut that piece in half. You'll use each piece along the long sides of your fabric piece.
Cut a second length of hem tape. This time, cut the tape to about 4-inches long, and then cut it in half. If your rip is very wide then you might need extra length, but for a normal rip that has very little width, the 4-inch piece should suffice. These two tape pieces will be used on the short sides of your fabric piece.
Insert the hem tape into the tear. Place the longer tape lengths along the long sides of the fabric piece, and place the short tape lengths along the short sides, creating a hem tape border around your fabric piece. Hold open or "tent up" the tear slightly to see where you're arranging the tape, but be careful not to add to the tear.
Turn on your iron and allow it to heat up. Apply the iron over the tear, letting the heat fuse the fabric patch into place.
Apply glue to the inside "flaps" of the tear, which has now been patched, but not closed. Use a cotton swab to get the glue on the interior edges of the flaps. Press on the flaps to adhere them to the patch beneath the tear.
If you can't find matching fabric for your upholstered piece, you may be able to cut some from a non-visible area of the piece, such as the underside or beneath cushions. As a last resort, you could also just try to match the main colour of your upholstered furniture piece instead of the entire pattern.