WASHINGTON—A member of the National Labor Relations Board fired by President Trump sued him Wednesday, setting up a high-stakes battle over whether federal law limiting the president’s power to remove top executive-branch officials is constitutional.

Gwynne Wilcox’s lawsuit is the first to challenge the president’s ouster of several members of independent boards — moves that appear to contravene a 1935 Supreme Court ruling.

Gwynne Wilcox said her NLRB removal "defies ninety years of Supreme Court precedent that has ensured the independence of critical government agencies."