They certainly used centre-grip shields, including both round shields of various sizes (often with a centre-grip of two straps attached to 4 bosses, as frequently used in much later Indian and Persian shields) and kite shields with (often) vertical central grips.

Most of the evidence is from art, and the artistic depictions can be ambiguous. All of the shields where it is clear how they were held are centre-grip shields, as far as I have seen. There are ambiguous shields that could possibly be strapped, but I know of no definitely-strapped shields that early. From the 15th century onwards, strapped shields appear in art, apparently with a variety of strap arrangements, including combined strapped/centre-gripped shields with 6 bosses (as used in some Persian cavalry shields of later date).

Whether or not shields are centre-gripped can sometimes be deduced from the position of the shield when held. Otherwise, a central boss or 4 small bosses usually mean it is centre-gripped. Sometimes the inside of the shield is clearly shown, which can provide unambiguous identification as a centre-grip shield. Ambiguous shields often have no bosses, and the position of the shield doesn't clearly indicate either centre-gripped or strapped.

Gorelik (1979) and Nicolle (1982) give many examples of shields in art.

There are very few relevant archaeological finds of shields. The only one I know of is a part of a wooden round shield, from Uzbekistan(?). This find is described in Encyclopaedia Iranica (Litvinsky, 2010) as

a unique finding of the shield of the late 7th-early 8th century at the castle on the Mug Mountain. The middle part of a wooden shield of rounded shape was found there, with diameter of 61 cm and thickness of 1.1 cm in the center and 0.6 cm at the edges. The shield consists of planks, 6 cm wide, which were glued onto each other and additionally fixed by metal rivets. Metal binding passed by the edge of the shield, and parchment was glued onto it from both sides. A metal handle was fixed to the rear side by tacks. The front side of the shield contains a painting of an armed horse-rider. The shield apparently belonged to a warlord and was several times used in battles. It has traces of arrows, but none of the latter pierced the shield through.

I have not seen any drawing or photo of the inside of the this shield, so don't know any further details about the handle.

References:

Michael Gorelik, "Oriental Armour of the Near and Middle East from the eighth to the fifteenth centuries as shown in works of art", pp 30-63 in Robert Elgood (ed), Islamic Arms and Armour, Scolar Press, 1979.

Boris A. Litvinsky, "SHIELD in Eastern Iran", Encyclopædia Iranica, online edition, 2010, available at http://www.iranicaonline.org/articles/shield-eastern-iran

David Nicolle, The Military Technology of Classical Islam, 3 volumes, PhD thesis, University of Edinburgh, 1982.