She became upset while singing the song REM from her Sweetener album at the Enterprise Center in St Louis, Missouri.
In a Twitter post that has since been deleted, she wrote: "I feel everything very intensely and have committed to doing this tour during a time in my life when I'm still processing a lot.
"So sometimes I cry a lot!"
Grande said she wrote the message "because I'm grateful and because I want you to know that if you too are hurting, you can push through and are not alone".
The singer has been open about her difficulties since a suicide bomber killed 22 people after her concert in Manchester in May 2017.
Also, her ex-boyfriend Mac Miller died last September, and her engagement to comedian Pete Davidson ended in October.
Referring to fans on her US tour, she said: "I'm not sure what I did to deserve to meet so many loving souls every night... but I want you to know that it really does carry me through."
Grande also wrote that her Sweetener tour was "a dream come true... no matter how hard it gets or how many feelings come up that are screaming at me to be processed and sorted through one day."
The singer added: "I'm grounded by gratitude and promise not to give up on what I've started."
She wrote: "It is hard to balance taking care of the people around you, doing your job, and healing/taking care of yourself at the same time... but I want you to know, you aren't alone and I think you're doing great. Love you."
The Sweetener tour began in March, and Grande will visit the UK and Ireland later this year, with dates in London, Birmingham, Glasgow, Sheffield and Dublin.
She will also headline Manchester Pride in August, returning to the city more than two years after the Manchester Arena terror attack and her subsequent One Love benefit concert.