Williamson missed their wins over defending champions England and the Netherlands to continue his rehabilitation from a knee injury he suffered in March that required surgery.
Experienced fast bowler Southee has been recovering following surgery on his fractured right thumb.
"Tim's progressing well, but won't be playing tomorrow's game," Williamson, who led his team to the final of the 2019 edition of the tournament, told reporters.
"As for my recovery, it's been quite a journey but largely a good one.
"...really excited to be named in the World Cup squad, be sitting here now and really excited at the prospect of tomorrow, which is another big challenge for us."
New Zealand fell agonisingly short of winning the title in 2019 when England were declared winners via the boundary countback rule after the heart-stopping final at the Lord's had ended in a tie.
Williamson said they drew inspiration from the All Blacks, New Zealand's three-time World-Cup winning rugby team, who face Ireland in the tournament's quarter-finals on Saturday.
"I think when we were growing up, we all wanted to be All Blacks and that couldn't happen so we tried something else," the batter said.
"We're here as a cricket team but I think something that you do hear often about their side is their culture, their environment, and their ability to keep moving forward as a team and adapting to what's in front of them..."
"And they keep doing really well at staying ahead of that curve."
Looking at their next match, Williamson said New Zealand could not afford to underestimate Bangladesh especially at a spin-friendly venue like Chennai.
"We come into this tournament knowing that anybody can beat anybody. That makes a really exciting event I think and the conditions are always going to change," he said.
"I think both teams have some good spin bowlers that no doubt will play a big part tomorrow."
