Encouraged to explore as a child by her late father, Dr. Eleanor "Ellie" Arroway (Jodie Foster) works for the Search for Extraterrestrial Intelligence (SETI) program at the Arecibo Observatory in Puerto Rico. She listens to radio transmissions hoping to find signals sent by extraterrestrial life. Science Advisor to the President David Drumlin (Tom Skerritt) pulls the funding from SETI because he believes the endeavor is futile. Arroway gains backing from secretive billionaire industrialist S. R. Hadden (John Hurt), who has followed her career and allows her to continue her studies at the Very Large Array (VLA) in Socorro County, New Mexico.

Four years later, with Drumlin seeking to close SETI, Arroway finds a signal repeating a sequence of prime numbers, apparently sent from the star system Vega. This announcement causes Drumlin and the National Security Council, led by National Security Advisor Michael Kitz (James Woods), to attempt to take control of the facility. As Arroway, Drumlin and Kitz argue, members of the team at the VLA discover a video source buried in the signal: Adolf Hitler's welcoming address at the 1936 Summer Olympics in Berlin. Arroway and her team postulate that this would have been the first significantly strong television signal to leave Earth's atmosphere, which was then transmitted back from the Vega star system, approximately 26 light-years away.

The project is put under tight security and its progress followed worldwide. Arroway learns that the signal contains more than 60,000 "pages" of what appear to be technical drawings. The reclusive Hadden secretly meets with Arroway on his jet to provide the means to decode the pages, found when they are arranged in three dimensions. The pages reveal a complex machine allowing for one human occupant inside a pod to be dropped into four spinning rings.

The nations of the world fund the construction of the machine in Cape Canaveral at the Kennedy Space Center's Launch Complex 39. An international panel is assembled to choose a candidate to travel in the machine. Although Arroway is one of the top selections, Christian philosopher Palmer Joss (Matthew McConaughey), a panel member whom Arroway met in Puerto Rico and with whom she had a brief romantic encounter, brings attention to her lack of religious faith. As this differentiates her from most humans, the panel selects Drumlin as more representative. On the day the machine is tested, a religious fanatic (Jake Busey) destroys the machine in a suicide bombing, killing Drumlin and many others.

A cancer-stricken Hadden, now in residence on the Mir space station, reveals to Arroway that a second machine is hidden in Hokkaido, Japan, and that Arroway will be its pilot. Arroway, outfitted with several recording devices, is locked into the pod of the Japanese machine, dropped into the spinning rings, and disappears. When the pod apparently travels through a series of wormholes, she experiences displacement and can observe the outside environment, including a radio array-like structure at Vega and signs of an advanced civilization on an unknown planet. Arroway finds herself in a surreal beachfront landscape similar to a childhood picture she drew of Pensacola, Florida, and a blurry figure approaches that becomes her deceased father (David Morse). Arroway recognizes him as an alien taking her father's form and attempts to ask questions. The alien deflects her inquiries, explaining that this journey was just humanity's first step to joining other spacefaring species.

Arroway considers these answers and falls unconscious. She awakens to find herself on the floor of the pod; the machine's control team is repeatedly calling for her. She learns that, from outside the machine, it appears the pod merely dropped through the machine's rings and landed in the safety net. Arroway insists that she was gone for approximately 18 hours, but her recording devices show only static. Kitz resigns as National Security Advisor to lead a Congressional Committee to determine whether the machine was a hoax designed by Hadden, who has died. Arroway asks the committee to accept the truth of her testimony on faith. In a private conversation, Kitz and White House Chief of Staff Rachel Constantine (Angela Bassett) reflect on confidential information that, although Arroway's recording device only recorded static, it recorded 18 hours of it. Arroway and Joss reunite, and Arroway receives ongoing financial support for the SETI program at the Very Large Array.