This leg will be Price's first involvement with Wales since he played in last year's Rugby World Cup in Moscow while Webber has not played since the first round of the series in Australia last October due to a groin injury.
The Japan leg will be held on 22-23 March at Tokyo's Prince Chichibu Memorial Ground before the series moves on to Hong Kong Stadium where the seventh leg of the world series will be staged between 28-30 March.
Injuries have forced Wales Sevens head coach Gareth Williams hand somewhat but he is confident the newcomers have what it takes to compete at international level.
"The injuries we've currently got have given a number of new faces an opportunity to go out and show what they can do," he said. "Owen Jenkins comes in after having some experience within the squad. He's been doing well with the Blues and now he has a chance on the international sevens stage.
"Ross Jones is fresh to the environment - he has been superb in training and is learning a lot. It's going to be exciting to see how he goes in tournament.
"It's great to have Alex back in the fold as he is a threat with the ball and it's good to have that option back in the squad."
This weekend Wales are grouped with series leaders New Zealand, Canada and Portugal where they face an uphill task to reach the knockout stages.
"There are no easy pools at this level. We are in with New Zealand who are the form side, Canada, who are coming off the back of tremendous performances in Vegas and Wellington and Portugal who are a dogged side to play against - we've had problems against them in the past but we've also done well against those teams in the past - it's exciting and we're looking to put our stamp on the group," said Williams.
"We want to progress to those quarter-finals to give ourselves an opportunity to progress further in the knockout out stages."
Wales Sevens squad for Japan/Hong Kong
James Davies (Captain) (Carmarthen Quins)
Sam Cross (Cardiff Met)
Iolo Evans (Carmarthen Quins)
Craig Price (Scarlets)
Jason Harris (Carmarthen Quins)
Tom Williams (Blues)
Rhys Jones (Cross Keys)
Ross Jones (Bridgend)
Will Price (Aberavon)
Owen Jenkins (Pontypridd)
Luke Morgan (Bridgend)
Alex Webber (Pontypridd)
13th man to travel: Aled Summerhill (Pontypridd)