Does the Constitution require that the Speaker of the House be an elected member of the House of Representatives?
It's not a must for the Speaker to be an elected Member of the House of Representatives. Anyway, every Speaker until now has been a Representative. Besides being the head of the House, the Speaker also heads the majority political party and accomplishes procedural and administrative functions.
Today's Speaker of the US House of Representatives is Paul Ryan, who assumed his office in the 29 of October, 2015 and replaced the previous Speaker, John Boehner.