Ticket holders are being asked to hold on to their purchased tickets, as they will remain valid for the new dates.
The tour was expected to kick off next Wednesday in Christchurch, then finish up in Wellington on Saturday, July 10.
Barnes debuted the title track from Flesh And Blood at the State Memorial Service for his close mate, Michael Gudinski.
"Michael's loss really hit us hard. Everything he did was about family one way or another which is probably why he liked that song [Flesh and Blood] so much. I'm dedicating this record to his memory."
In his homeland of Australia, Barnes has enjoyed 12 solo chart-toppers, plus five with Cold Chisel, taking his career tally to a record-setting total of seventeen #1 albums.
This is where the Covid-19 outbreak in Australia currently stands: NSW has 195 confirmed cases, Queensland has 20 cases, the Northern Territory has nine cases, Western Australia has four cases and South Australia has five cases.