Ariana Grande has indefinitely suspended her world tour in the wake of the terrorist bombing in England ... TMZ has learned.

Sources connected to Ariana tell TMZ, she will not perform Thursday in London and has decided for now to put the entire European tour on hold. She was scheduled to perform in England, Belgium, Poland, Germany and Switzerland.

Ariana just tweeted, "broken.  from the bottom of my heart, i am so so sorry.  i don't have words."

As we reported, Ariana is inconsolable ... "in hysterics" after the bombing. As one source said, she's incapable of performing for anyone. She and her team, we're told, are also deeply concerned about security.

Ariana's manager, Scooter Braun, said, "We mourn the lives of children and loved ones taken by this cowardly act," adding, "We ask all of you to hold the victims, their families, and all those affected in your hearts and prayers."

Our sources say Ariana is not concerned with her shows now ... she and her team will re-evaluate the touring schedule when she's emotionally ready.