Kyrgios, a surprise Wimbledon quarter-finalist, had been due to partner Casey Dellacqua in the international mixed team event, which begins in Perth on Sunday.
However, a back problem has ruled the 19-year-old out of the competition, giving Ebden - the world number 231 - a chance to impress.
A message from the Hopman Cup's official Twitter account confirmed Kyrgios' withdrawal.
Update: Nick #Kyrgios has been forced to withdraw from #HopmanCup due to a back injury. We welcome WA's own @MattEbden to replace him.
— Hopman Cup (@hopmancup) December 31, 2014Australia has been grouped with France, Great Britain and Poland in Group B and face the latter on Sunday.
