Halfback Moses will miss the first game of Jason Ryles' coaching tenure with a foot injury, with the Eels keen to take a cautious approach with their star playmaker.
"Mitch is experiencing soreness from a previous injury, we're taking a cautious approach to ensure his foot heals properly and he can play his best football for the team," Ryles said.
"We will continue to monitor Mitch's recovery and make an assessment on a return date next week."
Ronald Volkman will replace Moses in the halves on Sunday, but Brown will be expected to call the shots as uncertainty over the New Zealand Test five-eighth's future rumbles on.
Brown is the most experienced member of the Eels' spine, with Volkman, hooker Brendan Hands and fullback Isaiah Iongi boasting just 45 NRL games between them.
Jack Williams will debut from the second row for Parra, while Melbourne have thrown Stefano Utoikamanu straight into a starting front-row berth.
Utoikamanu's old club Wests Tigers kick off the Jarome Luai era on Friday with a fully fit squad at home to Newcastle in Campbelltown.
Luai will partner Lachie Galvin for the first time as one of six debutants alongside Jeral Skelton, Sunia Turuva, Terrell May, Jack Bird and Royce Hunt.
Newcastle, meanwhile, have named Phoenix Crossland, partnered Jack Cogger and Fletcher Sharpe in the halves and thrown ex-Canberra flyer James Schiller a debut on the wing.
Tyrell Sloan has to make do with a place in the reserves for St George Illawarra when they face Canterbury at Kogarah on Saturday.
In the day's later game, Jazz Tevaga has beaten Jake Simpkin to start at hooker for their home clash against North Queensland.
Meanwhile, the Roosters have named Mark Nawaqanitawase at centre, with Naufahu Whyte starting at prop in the absence of Spencer Leniu.
Friday night's clash at Suncorp Stadium between Wayne Bennett's South Sydney and his former apprentice Kristian Woolf's Dolphins has been postponed because of Tropical Cyclone Alfred.
