Maddux cited family reasons for his decision, putting out a statement through the Rangers.
"This afternoon I spoke with Ben Cherington and thanked him for the consideration to interview for the Boston Red Sox managerial post. It is humbling to know an organization with so much baseball history is interested in my services," Maddux said.
"I could give more reasons why an opportunity like this should be taken rather than not, but the reason for withdrawing my name from consideration comes down to a family decision. My wife and two daughters are together in the same state for the first time in three years, and words cannot describe my happiness. The game of baseball has many sacrifices, but being apart from family is the toughest. I feel there is too much distance between the Dallas-Fort Worth Metroplex and Boston to see my family as much as I'd enjoy.
"Again, I thank Ben Cherington and the Boston Red Sox for the flattery, honor, and compliment of considering me for their position."
Former Red Sox general manager Theo Epstein, who is now president of baseball operations for the Cubs, also requested permission to interview Maddux, and an interview with Chicago is scheduled for Wednesday.
The next candidate the Red Sox will interview will be Sandy Alomar Jr. on Wednesday.
The Sox interviewed Pete Mackanin and Dale Sveum for the manager's job last week.
Cherington said he would like to have his next manager in place by Thanksgiving.