Parisse was forced off in Italy's 29-0 defeat to France in Rome last week and has not recovered from his ankle injury in time, meaning Fijian-born Samuela Vunisa comes in at number eight.
Italy team manager Luigi Troiani explained: "Parisse has made a lot of progress since Sunday, he's walking normally... but to have picked him would have put his recovery at risk."
Haimona was dropped last week in favour of Tommaso Allan but, with the latter sidelined after suffering a hamstring tear in the defeat to France, the New Zealand-born number ten returns to rekindle his half-back partnership with Edoardo Gori.
Italy have also made two changes to the front row, with Martin Castrogiovanni returning at tighthead prop and loosehead Michele Rizzo coming in for Dario Chistolini, who drops back to the replacements bench.
Hooker Leonardo Ghiraldini takes over the captain's armband from Parisse.
Italy coach Jacques Brunel said: "Leonardo is one of the three vice-captains along with Marco Bortolami and (Quintin) Geldenhuys. He's the only one of the three in the starting XV, so the choice was logical."
Parisse's absence and Vunisa's switch to the number eight position means Brunel has brought Mauro Bergamasco in at openside flanker in what will be a rare start for the 101-times capped veteran.
Italy beat Scotland 22-19 at Murrayfield three weeks ago to claim their first win of the campaign but despite sitting second bottom of the table two points ahead of the winless Scots, they remain in danger of finishing with the wooden spoon for the second successive year. Scotland are at home to title-chasing Ireland in Edinburgh.
Brunel added: "We're disappointed with our performance against France because we wanted to confirm our good display against Scotland.
"I expect a difficult game on Saturday, but I also expect us to show what this team is capable of compared to our performance at the (Stadio) Olimpico last week."