Nadal begins his quest for a fifth title in Madrid later Wednesday against Italy's Fabio Fognini.
Kyrgios and Nadal have only met twice with the Australian making his breakthrough with a four-set win over the 14-time Grand Slam champion at Wimbledon in 2014.
Nadal, though, edged their only previous meeting on clay at the Rome Masters last year.
Fifth seed Milos Raonic is also into the last 16 as he got the better of a battle between two big servers 6-4, 6-4 over Giles Muller.
David Ferrer made it into round three without having to hit a ball as Jo-Wilfried Tsonga withdrew with a shoulder injury.
World number two Novak Djokovic begins life without long-term coach Marian Vajda later against Nicolas Almagro.