Little Hudson Doyle, from Hilsea, contracted Covid pneumonitis and is on a life support machine.
The six-month-old baby is being cared for at Southampton Children’s hospital, while his parents – Mariah and Liam Allen – stay by his side.
Heartfelt messages on social media and donations to their fundraiser have been pouring in since the tots condition was report.
In a joint statement, Mr and Mrs Allen said they were stunned by the response.
They said: ‘We are overwhelmed by the support we are receiving from everyone.
‘We are completely lost for words with everything that is going on at the moment, but just thank you a million times.’
Tiny Hudson was rushed to hospital on January 7, as he was struggling to breath and maintain oxygen levels.
He is currently on a extracorporeal membrane oxygenation life support machine (ECMO) – which pumps oxygen and blood round his body and breaths for him.
Heartbreakingly, doctors have given the baby a 50 per cent chance to live.
A GoFundMe page was set up to cover the family’s bills, and over £6,000 has been raised so far.
Levi Allen, Hudson’s grandad, said he was stunned by the support his family has gotten from the people of Portsmouth.
He told The News: ‘We've seen donations flooding in all through the day.
‘We initially set the goal at £2,000, as we didn’t know what was going on and I just wanted to help my daughter out.
‘I can’t thank the city of Portsmouth enough for coming together for my family.
‘When he comes home, I’m going to make sure he knows that the whole city was behind him and he won’t forget that at all.
‘I don’t think there are many cities that will come together as this city has for my family.
‘I didn’t expect anything like this, I’m stunned.’
Hudson remains in Southampton paediatric intensive care unit and his treatment is ongoing.
Residents have flocked to Facebook with kind-hearted messages of support.
Matt Underwood wrote: ‘Speedy recovery young man.
‘It was hard enough when our two-year-old boy caught it, thankfully mildly.
‘Well wishes and thoughts with you.’
Debbie Welch also commented: ‘Please keep fighting Hudson, you gorgeous little man.
‘I’m rooting for you my darling, sending you much love & preys that you make a full recovery asap x.’
Adele Marie Byng wrote: ‘My gorgeous baby cousin, get better soon and come home to your mummy daddy and big sister.
‘We need more cuddles xxxx.’
The fundraiser is at tinyurl.com/4zn7vs6w