He will be replaced by Café Rouge co-founder Karen Jones, who is also chairman of Hawksmoor and Mowgli.
Hendry Pickup, who joined Prezzo in July 2016, said he was leaving to pursue “other opportunities”. He will work in partnership with Jones through a transition period in April and May.
Like-for-like sales at Prezzo fell 8.1% in the year to December 2017, with the chain blaming rising costs and competition from brands such as Franco Manca and ASK Italian.
In March the group's creditors approved a CVA to close almost a third of its estate. The sites set to close include 62 Prezzo’s, the entire three-strong MEXIco brand, 28 of 31 Chimichanga tex mex restaurants, and the group’s only Cleaver grill in Cobham.
CVA documents revealed the group also owed banks and suppliers almost £220m.
Hendry Pickup has since launched a transformation plan that has seen top-performing sites rebranded with an improved layout.
“Under the stewardship of Jon and the rest of the leadership team, important steps have already been taken to move Prezzo forward,” says Jones.
“There is now a reshaped estate of excellent sites filled with skillful people ready to create something compelling together.”
Prezzo is owned by private equity firm TPG, which bought it for £304m in 2015.