Bench coach Kirk Gibson will take over as manager, and Jerry Dipoto, vice president of player personnel, will take over as GM, both on an interim basis.
"Their dismissal is a significant decision, but one that we find necessary in order to achieve a direction of winning consistently on the field again," Diamondbacks managing partner Ken Kendrick said in a written statement. "We have a number of talented players, but obviously see great room for improvement."
Byrnes had five-plus years remaining on the eight-year contract he signed before the start of the 2008 season. Hinch, who replaced Bob Melvin in May 2009, was signed through 2012.
The Diamondbacks, who have been paying off deferred salaries of several players since winning the World Series in 2001, will be responsible for paying Byrnes and Hinch the remainder of their salaries.
Hinch, who was promoted from farm director despite having no prior coaching or managerial experience, went 89-123 in his short stint as manager.
Byrnes, an assistant under Boston GM Theo Epstein, was hired in October 2008. In his second full season, the team won 90 games and advanced to the National League Championship Series. Byrnes was given a small ownership stake in the team when he signed his contract extension.
Since going 20-8 to begin the 2008 season, the Diamondbacks, despite having several young stars on the field, have limped to a 163-212 record.
They are 31-48 entering a 10-game homestand that begins this weekend with a three-game series against the Dodgers.
--RHP Edwin Jackson will start Friday night against the visiting Dodgers in his first appearance since throwing a no-hitter June 25 against the Rays. Jackson was pushed back two days from his normal workday because he threw 149 pitches (and walked eight batters) in the game, the most by a major league pitcher in five seasons. In his last eight starts dating to May 17, Jackson is 4-1 with a 2.51 ERA, and opponents are batting .200 against him during that stretch.
--RF Justin Upton has hit safely in 14 of his last 18 games at a .358 clip (24-for-67) with four doubles, four homers, nine RBI and nine walks. He also has reached base via a hit or a walk in 16 of his last 18 games, including a stretch of 13 straight that ended June 28.
--LHP Dontrelle Willis accepted his new role as a relief pitcher with no complaints. "I think it'll help me get myself right, get my arm slot back to where I want it to be," he said. "I can't continue to walk guys and expect to win. You have to put somebody in there who will throw strikes." For the time being, rookie RHP Barry Enright has assumed Willis' spot in the rotation.
--RHP Brandon Webb threw his latest bullpen session Wednesday and looks set to next face hitters for the first time as he continues his comeback from a shoulder problem that has kept him from pitching in a game for the past two years. Webb has said he will pitch for the Diamondbacks this season, but he still remains several days away from beginning a minor league rehab assignment and likely will need multiple outings before he can pitch in the majors again.
--1B Adam LaRoche has hit safely in all nine games against the Cardinals this season, batting .351 (13-for-37) with three home runs and 10 RBI.
--With a 4-2 victory Wednesday in St. Louis, the Diamondbacks snapped a streak of 12 consecutive road losses to National League teams.