Republicans are seeking to protect their narrow US House majority in next year's midterm elections.
President Donald Trump has championed the redistricting plan, telling reporters he expects the effort to yield as many as five additional House Republicans.
Republicans hold a narrow 220-212 majority in the House of Representatives, with three Democratic seats vacant after members' deaths.
Democratic Representative James Talarico said the redistricting plan amounted to "rigging" the 2026 elections.
"My Democratic colleagues and I just left the state of Texas to break quorum and stop Trump's redistricting power grab," Talarico said in the video posted on X on Sunday.
Several other Texas Democrats said on X they were headed to Illinois, whose governor is Democrat JB Pritzker.
Republican Governor Greg Abbott said in a statement on Sunday that any Democrat House member who didn't return would be removed from the Texas House.
"Democrats hatched a deliberate plan not to show up for work, for the specific purpose of abdicating the duties of their office and thwarting the chamber's business", the governor said in his statement, adding that leaving amounted to an abandonment of the office.
States are required to redistrict every 10 years based on the US Census but the Texas map was passed just four years ago by the Republican-dominated legislature.
While mid-cycle redistricting occasionally takes place, it is usually prompted by a change in power at the legislature.
Republicans have pursued redistricting in a special legislative session that will also address funding for flood prevention after the deadly July 4 flash flooding that killed more than 130.
Under the current lines, Republicans control 25 seats, nearly two-thirds of the districts in a state that went for Trump last year by a 56 per cent to 42 per cent margin.
Redistricting experts have said the plan could backfire if Republicans try to squeeze too many seats out of what is already considered a significantly skewed map.
14°C