It's a well known historical fact that as a result of this invasion, the kick-off for Operation Barbarossa was delayed. EDIT: Apparently several military historians are of differing opinion on this fact; so its not settled in any way.

The actual reasons for the invasion are less commonly known, besides the obvious Italian disaster in Greece. Here are some implications; Britain was now deploying its forces in Greece, the Albanian border was considered cluttered and poor terrain to invade, as it would necessitate 'moving through' the Italian units there, and most of the Greek efforts were focused on that front.

The presence of British forces so close to Romanian oilfields, the embarrassment of Axis force-of-arms, and the military overthrow of the pro-Axis Yugoslav government, are all used as arguments for the necessity of the invasion. What's worse, the Germans believed that the coup was heavily influenced by communist elements.

Here's a strategic consideration: Had Yugoslavia not been invaded, it would have interposed a government unfriendly to the Axis cause between the struggling Italians in Greece, and the Germans gathering to push into Soviet Russia. What if this same Yugoslavian government was brought into the Alllies? To a German strategic planner, the possibility of a soft underbelly was absolutely unacceptable; especially when considering the massive scale and ambition of Op. Barbarossa. It was therefore not only deemed a necessity but a convenience, it would provide security and a firm anchor to the Southern tip of Operation Barbarossa, remove a hostile-if-neutral government, and allow German units to punch through to the rear of the bulk of the Greek deployment and kick out the British from the Balkans.

Sources:

"Terror in the Balkans : German armies and partisan warfare" Sherpard, Ben - Harvard University Press 2012

"War and revolution in Yugoslavia, 1941-1945 : occupation and collaboration" Tomasevich, Jozo, Stanford Uni Press, 2001

"Invasion Balkans! the German campaign in the Balkans, spring 1941" Blau, George E. Burd Street Press, 1997