2:26 PM PT -- David Allen tells TMZ his daughter Lily Grace passed away in her sleep unexpectedly.

The infant daughter of TikTok star David Allen has passed away ... the Internet personality confirmed in a new statement.

The social media sensation -- best known as "ToTouchAnEmu" online -- took to TikTok and Instagram Sunday and uploaded a heartbreaking update, in which he shared that his newborn daughter, Lily Grace, had died on July 27.

According to David, Lily Grace died at midnight last week ... but he waited to announce the news publicly as he was struggling to process the loss.

He added ... "I have cried every tear I can possibly cry, I think. It's not easy. I don't wish this on anybody."

David and his wife, Jessica, welcomed Lily Grace back on June 21 ... with her birth announcement being shared on Instagram. At the time, David joked he planned to farm "content" of his daughter moving forward.

The TikTok star went on to share one small update about Lily Grace a few weeks later, as he posted a video of his newborn watching YouTube's "Technology Connections" instead of the parenting-favorite "Ms. Rachel."

As David concluded his somber message, he encouraged his followers to hug their little ones tight ... and to donate to Dallas Children's Hospital in Lily Grace's name.

Lily Grace's memorial service will be held on Tuesday, David confirmed ... but asked fans to please not show up if they weren't issued an invitation.

Lily Grace was only 5 weeks old. A cause of death was not shared.

RIP