Upon finding Juliet, her parents think she committed suicide.  She drank from a vial and they probably feel it was a poison or very strong medicine that killed her.  They also feel she was very distraught over the death of Tybalt and this probably added to her distress.

They don't actually say what they think she died of in Act IV, Scene 5, but in Act V, Scene 3 when Paris sees Romeo trying to get into the Montague tomb, we learn what everyone thinks that she has died from.

Paris:
This is that banish'd haughty Montague
That murder'd my love's cousin,--with which grief,
It is supposed, the fair creature died,--
And here is come to do some villanous shame
To the dead bodies: I will apprehend him.--

Paris says that is supposed, and I'd assume this is from her family and himself, that they believe that Juliet has died of grief resulting from Tybalt's death

Strangely enough, Lord and Lady Capulet never mention what Juliet's cause of death in act four, scene five. They are so overcome with grief at the discovery of their daughther's still body. As the audience, we don't share that grief since we know why she is "dead". If we have to guess, it may have been grief over Tybalt's death that caused her death, whether it be a suicide or natural causes.