Hi Bob
The following is based on the paper "The Gentry of Bedfordshire in the 13th and 14th Centuries" by Katherine S Naughton (Leicester University Press 1976), and as the title implies refers mainly to Beds, but the conclusions probably hold good for the rest of England.
Katherine says that in 1066 a knight was a not very important unit in the feudal army, but by the end of the 13th century he had become a man of considerable social and economic distinction, whose activities were primarily administrative. During the 13th century there developed a split in the knight's functions, until by 1300 they could be divided into fighting knights and the rest, who were shire administrators.
The sheriff was appointed by the king, and by the 14th century was usually for a term of one year, although men could serve more than once. As the opportunity to make ill gotten gains was considerable, in the 12th and 13th centuries men were prepared to pay well to secure this office. The sheriff was the chief shire official throughout the Middle Ages.
In Beds, out of 27 sheriffs researched, 23 were definitely knights, 3 probably were, and one was an esquire.
So the quick answer to your question is that it doesn't seem as though it was it was an absolute requirement to be a knight to hold the office of sheriff, but in practice most of them seem to have been knights
David