If the present SMBH is the outcome of a merger between two black holes, the merger process can cause the resulting SMBH to receive a “kick” due to the emission of gravitational waves. The “kick” can displace the SMBH from the center of M87. Depending on the merger process, the SMBH can remain displaced from the center of the galaxy for millions to billions of years.
The nucleus of M87 has a highly-collimated, relativistic jet of matter extending outwards for thousands of light years. This jet is made up of material ejected from the galaxy by the SMBH. Since the displacement of the SMBH from the center of M87 is in the counter-jet direction, acceleration of the SMBH by an asymmetric jet (i.e. jet is stronger in one direction) can result in the observed displacement if the jet is long-lasting and if the restoring force exerted by the galaxy on the SMBH is small.
Batcheldor et al. (2010), “A Displaced Supermassive Black Hole in M87”, arXiv:1005.2173 [astro-ph.CO]