Her decision leaves Republicans to choose between Mia Love and Bob Fuehr, both of whom have been in the race for months. On the Democratic side, the candidates are Doug Owens and Bill Peterson.
Matheson, who beat Love in 2012 by less than 800 votes out of more than 245,000 cast, has decided not to see re-election this November, though he has said he may run for governor or senator in 2016.
Love, the former mayor of Saratoga Springs, is widely seen as the frontrunner, having claimed the Republican nomination last time. She is the most widely known of the candidates and she has the most campaign resources, disclosing more than $700,000 at her disposal at the start of the year. Fuehr, a former business executive for telecom giants, ran for Congress in the 2nd Congressional District in 2012, but didn't make it out of the Republican convention.
Johnson, who was elected to the state school board in 2012, said she didn't consider running for Congress until some advisers, whom she refused to name, encouraged her during the candidate-filing period.
"I think it is good for there to be choices in races, along with Bob Fuehr and Mia Love, an additional choice may be healthy and helpful," she said.
Johnson attended one meet-the-candidates night in Lehi, but in the days that followed decided that she wasn't willing to let go of her school-board responsibilities, which includes hiring a new superintendent after Martell Menlove unexpectedly retired. She also said it wasn't good timing for her clients at Coraticum Asset Management, where she serves as president.
In a letter to delegates, Johnson said: "As much as I would like to engage fully in giving 4th District voters another option, recent developments have made it clear that my priority must be to continue serving on the State Board of Education and in the community."
Johnson is not endorsing either Love or Fuehr at this time, but said she hopes a Republican claims the House seat created in 2011 following redistricting.