Rodriguez, 59, was one of six Democrats who filed to run in the special election in 23rd Congressional District, which has been represented by Bonilla, R-San Antonio, since 1992 when he was first elected.
"I'm not going to be running and that's my decision based on family and personal reasons," Rodriguez said.
"I don't want that to be construed that Bonilla, that no one can take him, because he's vulnerable."
The district is one of six holding special elections Nov. 7, the same day as the general election.
A federal three-judge panel redrew the districts this month in response to a June Supreme Court ruling that said a 2003 redistricting of Texas' congressional map — led by former House Majority leader Tom DeLay — created a 23rd District that violated the Voting Rights Act by diluting Hispanic voting strength.
The special races pit all certified candidates against one another in each district, regardless of party. If no one gets more than 50 percent of the vote, the top two vote-getters in each district will face each other in a runoff in December.
Rodriguez served in Congress from 1997 to 2005. His campaign was $80,000 in debt at the end of June, but Rodriguez said earlier this month that had been reduced to $7,000.
Rodriguez twice lost in Democratic primaries to Rep. Henry Cuellar, D-Laredo, in the 28th District, but with the newly configured district found himself in the 23rd.
One independent, Craig T. Stephens, 47, also filed to run in the district.
The other Democrats who filed to run in District 23 are August G. "Augie" Beltran, 58; Rick Bolanos, 57; Adrian DeLeon, 31; Lukin Gilliland, 54; and Albert Uresti, 51.
Texas Secretary of State Roger Williams will certify the names of candidates by Sept. 6.
Bonilla is seeking an eighth term. The district stretches from San Antonio to the Texas-Mexico border and out to far West Texas.
Under the new map, Bonilla's district includes the heavily Hispanic and Democratic neighborhoods of south Bexar County, and includes part of his hometown of San Antonio, where his mother still lives.
Before the GOP-led Texas Legislature redrew the lines in 2003, Bonilla's support among Hispanics in his district was slipping. The lines were reconfigured, scooping some Laredo Hispanics into Cuellar's neighboring district, to give Bonilla an edge over a Democratic candidate. He won re-election under that plan in 2004.
Cuellar's district now includes all of Laredo and Webb County.
The new 23rd District has 61 percent Hispanic voting-age population, compared to the 51 percent Hispanic voting-age population in the district in which Bonilla was elected.