Pakistan will play five one-dayers and two T20 internationals.
After a dismal performance at the Champions Trophy last month, Malik and Kamran had to face the brunt along with opener Imran Farhat, who fared badly in the three group matches.
While opener Ahmed Shahzad, allrounders Sohail Tanvir and Hammad Azam have been recalled by the selectors, uncapped players Haris Sohail, Zulfiqar Babar and wicketkeeper Rizwan Ahmed are also part of the squads.
Qasim said the trio was dropped because of poor form but could make comebacks with strong performances in domestic cricket.
"It is not the end of the road for them they have served us well in the past and they can always come back," he said.
On Afridi's recall, the chief selector said: "We can't just drop all seniors and put pressure on the new players or youngsters. We also feel that wickets in the West Indies are doubled paced and there is low bounce and Afridi can not only shore up the lower order but also be effective as a bowler on such pitches.