Johnson, 32, arrived at Bears' headquarters on Saturday and signed a contract that likely will keep him with the team for just one week. Maynard's injury, suffered late in the week, is not believed to be serious, but the Bears will err on the side of caution, rather than have the strained groin become a lingering problem.
Chicago special teams coach Dave Taub was an assistant on the Philadelphia staff in 2003, which was Johnson's first season with the Eagles, and so he is familiar and comfortable with the five-year veteran.
Johnson was released by the Eagles on Sept. 1 after a training camp and preseason competition with free agent Sav Rocca, a former Australian Rules Football star. Although their statistics were fairly similar, the Eagles' coaches opted to go with the 32-year-old Rocca.
In 56 games, Johnson has a 41.6-yard gross average and a net average of 37.8 yards on 276 punts. The former Northern Colorado standout is regarded as a very good directional and hang-time punter.
Sunday's game will mark the first contest that Maynard has ever missed in his 11-year NFL career.
Maynard, 33, was said to be optimistic late in the week that he would be able to kick, but the Bears decided to be judicious and give him another week to rehabilitate.
The former Ball State star, a third-round pick by the New York Giants in the 1997 draft, has appeared in 161 games. He has a gross average of 42.2 yards and a net average of 38.1 yards on 920 punts. Maynard, who signed with Chicago as a free agent in the spring of 2001, has 291 kicks inside the opponent's 20-yard line and only 79 touchbacks.
Len Pasquarelli is a senior NFL writer for ESPN.com.