Denly, who made his debut last year, averages 29.53 in 15 Tests and has failed to capitalise on good starts. His highest score of 94 came against Australia in 2019.
The Kent batsman has been replaced in the 14-man England ODI squad by Lancashire's Liam Livingstone.
The likes of Jofra Archer, Ben Stokes, Jos Buttler and Chris Woakes will however miss the series owing to their red-ball commitment.
While Joe Denly will join the limited-overs training group for Ireland series, the other four players will return to their respective County sides.
Besides Denly, Dan Lawrence, Craig Overton, Ollie Robinson and Olly Stone are the four other players to have been released
The 34-year-old Denly, who has played 15 Tests for England, was dropped from the ongoing second Test against the West Indies after scoring 18 and 29 in the two innings respectively in the series opener at Southampton.
Young batsman Zak Crawley will retain his place in the playing XI for the second Test following his impressive 76 in Southampton.
Gough also raised questions on the selection of Joe Denly, who scored 18 and 29 in the first Test.
Denly could manage only 18 and 29 in the first Test against the West Indies at the Ageas Bowl. He has not passed the 50-run mark in his last eight innings.
Former England captain Nasser Hussain cited examples from Virat Kohli and Ben Stokes to urge Joe Denly to tinker with his technique.
Only 82 minutes of play was possible, all of it in the second session of the day in which 17.4 overs were bowled.
This implies that Zak Crawley will have to make his way for Root's inclusion in the second Test against West Indies
Thirty-four-year-old Denly is expected to cover for regular Test skipper Joe Root in the series opener, who left the bio-secure bubble and returned to Sheffield to be at the birth of his second child.
Joe Denly dropped Kane Williamson on 62 during the final day of the second Test at Hamilton.
At stumps, England were 241/4 with Ben Stokes and Ollie Pope remaining unbeaten at the crease on 67 and 18, respectively.
Denly made a half-century on his return against New Zealand A in the warm-up game here.
Jonny Bairstow was left out of original Test squad after poor performances in the Ashes, where he averaged just 23.77 from five matches.
England have not called up his replacement for the four remaining matches in the series, which they currently lead by 1-0.
England skipper Eoin Morgan stated that ruling Denly and Willey out from the final World Cup squad was his 'toughest decision ever' but at the same time backed it by calling it a 'right call'.
Jofra Archer replaced David Willey while Liam Dawson and James Vince came in place of Joe Denly and Alex Hales respectively.
Top News
Latest News
