It is understood that the West Indies coaching staff has one eye on the ODI World Cup qualifiers in February 2027, with the duo seen as important cogs in the white-ball team.
A Cricket West Indies (CWI) statement said that paceman Joseph was not selected "following a routine medical assessment and specialist consultation".
CWI release said: "While he is not ruled out from shorter formats, the medical team has stated that the demands of two consecutive Test matches in Bangladesh, which require fast bowlers to sustain repeated high-intensity spells over extended periods, present a significantly greater workload and injury risk than the shorter white-ball formats.
"Joseph will continue working with the CWI medical team and specialists in preparation for a full return to the longer format."
Opening batter John Campbell makes a return to the Test squad after recovering a hamstring injury while allrounder Keemo Paul has been named as Joseph's replacement.
The two-Test series in Bangladesh will be West Indies' last assignment for the ongoing 2025-27 World Test Championship (WTC) cycle. They currently sit eighth on the points table.
West Indies Test squad: Roston Chase (captain), Jomel Warrican (vice-captain), Joshua Bishop, John Campbell, Tagenarine Chanderpaul, Joshua Da Silva (wk), Justin Greaves, Kavem Hodge, Amir Jangoo (wk), Shamar Joseph, Brandon King, Keemo Paul, Kemar Roach, Jayden Seales, Kevin Wickham
Shai Hope hit yet another century while Keema Paul bagged a five-wicket haul as West Indies beat India by 24 runs in the fourth T20I in Hyderabad to level the five-match series at 2-2.
India regained the lead in their five-match T20 international series against the West Indies after Abhishek Sharma's explosive half-century and a disciplined bowling performance secured a 14-run victory in Indore on Sunday.
Shai Hope continued his fine form with an unbeaten century as West Indies pulled off their highest-ever T20I run-chase to beat India by six wickets and level the five-match series at 1-1.
Shreyas Iyer struck his maiden T20I century as India thrashed the West Indies by eight wickets with more than five overs to spare in the first game of the five-match series in Lucknow on Tuesday.
