The lawsuit, filed in a federal court in Washington against the Department of Health and Human Services and the Department of Treasury, targets a decision to delay implementation of the law's employer mandate, which requires employers with more than 50 employees to offer healthcare coverage.
It also challenges a provision of the law that authorizes Treasury payments to health insurance companies.
House Speaker John Boehner, in a statement, said that Obama had bypassed Congress to take "unilateral actions" when implementing the healthcare law, also known as Obamacare.
"If the president can get away with making his own laws, future presidents will have the ability to as well. The House has an obligation to stand up for the Constitution," Boehner said.
Jonathan Turley, the lead counsel for House Republicans on the lawsuit, said in a Friday blog post that the president's actions blurred the lines between branches of government and usurped the ability of Congress to use the "power of purse" during the appropriations process.
The House had passed a resolution in July authorizing the lawsuit.