Launchbury has succumbed to a fibia stress fracture, while Marler is out due to personal reasons.
Jones will turn to Charlie Ewels and Tom West, who both link up with the squad at St George’s Park on 27 January to begin preparation for the tournament opener against Scotland.
“Always grateful for the opportunity so not an easy decision, but want to do right by my family in these crazy times and won't be meeting up with the squad for this tournament,” Marler said on social media. “Look forward to watching the team rip in. Go well Rose.”
Launchbury’s setback is a cruel blow at a time when he had established himself in Jones’ second row alongside Maro Itoje.
"We were on an artificial surface the other day for the first time and whether that has aggravated it slightly.....Joe spoke to us after that," Wasps head coach Lee Blackett said.
"We wanted to scan it and make sure it wasn't serious, but it's come back like this. We fully expect him to be out for up to six weeks.
"He will stay with us and our medics and we'll try our best to get him back for the last couple of games of the Six Nations, that's our aim for Joe."
It is West’s first senior call-up after impressing for Wasps, while Bath’s Ewels has 17 caps.
England will take on Scotland at Twickenham on 6 February, with kick-off scheduled for 4:45pm.