The 50-year-old gave birth to her first son, Eissa, on 3 January. In a video message to fans, she described him as "so healthy, so beautiful, so sweet, so loving, such a happy baby".
She also addressed her separation from the baby's father, Wissam Al Mana.
"We are in court and the rest is in God's hands," said Jackson.
As for the tour, it will resume on 7 September in Lafayette, Louisiana, followed by a further 55 dates in the US and Canada this autumn.