The show follows an actress named Suzie Pickles, played by Piper, whose life is disrupted when her phone is hacked and compromising images of her are shared publicly.
The trailer sees Pickles in a chaotic spiral as the hacking unravels every aspect of her life.
Sky describes the show as a drama about “the moment in life when the mask slips, asking if any of us can survive being well and truly ‘known’.”
Daniel Ings (The Crown), Leila Farzad (Innocent) and Nathaniel Martello-White (Silent Witness) also star.
Co-created by Piper, the series is written by her friend and collaborator Lucy Prebble, writer/co-executive producer of Succession and creator of Secret Diary of a Call Girl.
Announcing the show last year, Piper said: "It's taken years to finally get Lucy, my long-term GF and favourite writer in London - to work with me again. We feel we've created something timely and not for the faint-hearted.
"If you too suffer with anxiety, shame, compulsive lying - but like a laugh - please tune in at some point."
Prebble was also this week awarded the inaugural Michael Billington award for best new play for A Very Expensive Poison.
I Hate Suzie is one of 80 Sky original shows debuting in 2020, with other titles including Breeders (starring Martin Freeman) and Two Weeks to Live (starring Maisie Williams and Sian Clifford).
Billie Piper recently made her directorial debut with Rare Beasts, starring Lily James and David Thewlis, which premiered at Venice Film Festival in 2019.