Born in Pakistan in 1947, Sheikh received a Master of Arts in economics from McMaster University in 1970, and earned his doctorate in economics from the University of Western Ontario in 1973. He is married with 3 children.
Sheikh began his public service career as an economist with the Economic Council of Canada from 1972 to 1976. After a brief stint with the National Energy Board between 1976 and 1978, he joined the Department of Finance and rose to the rank of Senior Assistant Deputy Minister in 2000.
Between 2001 and 2006, he held senior positions with Health Canada, the Privy Council Office and Human Resources and Social Development Canada. He has also taught at the University of Ottawa and Carleton University. Later in his career, Sheikh oversaw a $100-billion tax-reduction policy and helped craft the 2005 budget. He was praised by a former colleague as "the best economist in the federal government."
Sheikh was appointed as the head of Statistics Canada by Prime Minister Stephen Harper. He officially became the Chief Statistician of Canada on June 16, 2008, replacing Ivan Fellegi.
On July 21, 2010, Sheikh resigned from that post, following a controversy resulting from the Conservative government's decision to no longer require mandatory completion of the Canada 2011 Census long form. The decision has been heavily criticised; opponents have argued that the decision was politically motivated and that it will compromise the value of census data.