Wood's inclusion is the only change from the team which secured a famous final-session victory against Pakistan in Rawalpindi in the first Test.
Ollie Pope has retained the gloves in place of specialist wicketkeeper Ben Foakes. Foakes was unwell and unable to play in the first Test, with Pope standing in for his Surrey teammate.
Stokes has decided to retain Pope in the role in Multan but insists Foakes is still the number one wicketkeeper in the squad.
"The communication to Ben was that the real positive for him to take out of this selection is that it's just for this Test match," said Stokes.
"Foakesy still is the number one gloveman in England and I'll still keep saying it that he's the best keeper in the world. It must sound a bit silly to not be picking him, but you've got to look at the conditions we face out here.
"Pakistan is a very hard place to come and bowl. Adding Mark Wood into the side gives us the best opportunity to take 20 wickets. That's what we came here to do. We came here to try and win games of cricket.
"We want to keep continuing to press the way that we play and we felt bringing Woody into the team was the best opportunity for us to do that out here in this specific Test match."
Wood was not available for the first Test as he continued to recover from an injury sustained during England's victorious T20 World Cup campaign in Australia.
Stokes brought him into the squad and believes the pace bowler can add a new dimension to the England bowling attack.
"Having someone in your squad who can bowl 150km/h is a massive bonus for any team around the world, especially out here with Pakistan being a very hard place to come and win," he added.
"Having someone of this calibre and what he brings, the way in which he bowls, is going to massive for us. He is going to add to our ability to take 20 wickets I think, and it's a bit of a different story to having three low 80mph bowlers compared to Mark Wood bowling."
Livingstone returned to the UK after injuring his right knee during the first Test.