The probe is created to study the sun's ultra-hot outer atmosphere, called the corona, among other mysteries of our star.
The journey, called the Parker Solar Probe, will loop around the sun 24 times, flying within the star's hot million-degree atmosphere.
The heat shield is built to withstand radiation equivalent to up to about 500 times the Sun's radiation on Earth.
"All I can say is, 'Wow, here we go.' We're in for some learning over the next several years", said Dr Parker, who proposed the existence of solar wind - a steady, supersonic stream of particles blasting off the sun - 60 years ago.
Greeting the launch - on the back of a mammoth Delta-IV Heavy rocket - NASA tweeted: "3-2-1... and we have liftoff of Parker #SolarProbe atop @ULAlaunch's #DeltaIV Heavy rocket".
A Sun-skimming mission like Parker Solar Probe has been a dream of scientists for decades, but only recently has the required technology - like the heat shield, solar array cooling system, and fault management system - been available to make such a mission a reality.
That's where it will encounter temperatures of almost 2,500 degrees Fahrenheit. The probe is set to make 24 passes through the corona collecting data.
NASA Nasa's Parker Solar Probe is humanity's first-ever mission into a part of the Suns atmosphere called the corona
"We are ready. We have the flawless payload". A key question that the probe seeks to answer is how solar wind is accelerated, and for the first time it will be able to look for answers at the source of solar wind itself.
A triple-core Delta IV Heavy rocket blasted off from Cape Canaveral just after 3:30 a.m. Sunday, momentarily turning night into day in a spectacle visible for miles along the Florida coast.
"I really have to turn from biting my nails and getting it launched to thinking about all the interesting things which I don't know yet, and which will be made clear, I assume, over the next five or six or seven years", Parker said.
The spacecraft is the only NASA probe in history to be named after a living person - 91-year-old solar physicist Eugene Parker, who first described the solar wind in 1958.
Zurbuchen considers the sun the most important star in our universe - it's ours, after all - and so this is one of NASA's big-time strategic missions.
The spacecraft, which will plunge into the sun's atmosphere, known as the corona, is protected by an ultra-powerful heat shield.
PSP is carrying four instrument suites created to study the sun's magnetic fields, plasma and energetic particles, and image the solar wind.
"We'll also be the fastest human-made object ever, travelling around the Sun at speeds of up to 690,000km/h (430,000mph) - NY to Tokyo in under a minute!" she told BBC News.