Announcing their departure from the app, where they have 3.2 million followers, they wrote: "We need to fix our family so after today we are taking time to get our [selves back] together."
They also posted an emotional video on Facebook, saying: "I'm sorry it's come to this but we need time for our family to decide if and how we move forwards with social media. So for now... Good night beautiful people!"
Dad Nick Smith, 33, said the past week had been 'too much', explaining: "This past week I've tried filming, I've tried getting in the spirit of it, but at the minute the happy bit has gone. It's been taken away."
He added: "It's not fun for my family anymore, so I don't know where this will go.
"All I have to say now is, good night beautiful people."
The post also featured a compilation of clips from their favourite TikTok moments.
The family, who live in Welling, south east London, believe their home was torched because of their new-found fame online through 'funny' and 'heartwarming' videos.
Speaking after the incident, Nick - who previously worked seven days a week bricklaying before finding success on social media - said: "We don't see ourselves as famous or anything we're just a family who've gained a bit of a following and we've been targeted.
"I just think it's jealousy. Most people would be happy for others when they do well, but others are jealous."
As the fire broke out, Nick grabbed his daughters - Isabella, nine, and Amelia, six - and his six-week-old baby Teddy.
"My daughter wants to come home," he said.
"She doesn't understand why we can't come back."
Nick said people were 'very loose' on social media with their comments, and believes users can be 'really nasty'.
He added: "At the end of the day it could have cost people's lives.
"If that had been a petrol car it would have exploded and it would have been like a small bomb going off."
Four fire engines and around 25 firefighters were called to tackle the blaze on Wednesday 14 July after London Fire Brigade's 999 Control Officers took a total of 16 calls.
CCTV footage showed suspects setting fire to a Ford S-Max on the drive outside the semi-detached home of The Smithys - who live in Welling, south east London - between 10.30pm and 11pm on Wednesday 14 July, having allegedly used a milk carton filled with petrol.
Their neighbours came to the family's aid, helping carrying the children over the back garden fence to safety.
The Met Police said it is investigating the incident.
Det Sgt Danny Banks, from the Met's serious and complex investigations unit, said his team had been 'working around the clock' to find out what happened.
He said: "My heartfelt sympathies go out to them during what has been an unimaginably difficult time. I thank them for their continued support as enquiries are ongoing.
"This incident has been well publicised and whilst we appreciate that the public wish to support the family, we ask that all information is provided to us directly.
"I also urge the public to refrain from undertaking their own investigations in relation to this case."
Featured Image Credit: Facebook/The Smithy Family