A twisted knee sustained in training on Thursday sidelined him alongside fellow injured team-mates Ellis Harrison and Ben Close.
Hackett-Fairchild’s sole appearance since his January arrival from Bromley was a Leasing.com Trophy outing at Walsall in the same month.
Portsmouth transfer news: Blues receive bids for former Luton and Millwall midfielder
'Is proving one hell of a signing.... A real livewire' - Portsmouth match ratings from 2-0 win at Cheltenham
Transfer gossip: Portsmouth eye raids for ex-Chelsea man and Charlton Athletic's former Wigan Athletic midfielder
Former Portsmouth pair help Ipswich flex muscle as Norwich City man is slammed for conduct in Peterborough's Plymouth Argyle reverse
14 splendid photos from Portsmouth’s 2-0 win against Cheltenham in sun-soaked League One encounter
Since then first-team opportunities have been disrupted by injury and lack of selection.
Jackett told The News: ‘Reeco, Ben and Ellis all have slight knocks, we are not anticipating any of those being too long.
‘They are enough to keep the three of them out of the end of this particular week. By the time next week comes we think they will be fit.
‘Reeco has had a frustrating time since he has been here – and on Thursday twisted his knee.
‘Firstly he had the hamstring injury in and around when he signed. Then, in the build up to the play-off games, he injured his calf.
‘Now he has twisted his knee, although this time it’s a minor one.
‘Hopefully Reeco can get over it quickly and contribute in pre-season.
‘Although we haven't seen a lot of him yet, we just have to be patient and keep going with him.’
Watching the action on the training pitch at the Five Lakes resort in Maldon, Essex, were injured trio Hackett-Fairchild, Close and Harrison.
The trio could be back in action for next weekend, when the Blues face their second friendly.
Jackett added: ‘Ellis hasn’t trained with a calf strain. He has been out a week now, but has still been with us at Five Lakes.
‘Ben Close trained until Friday and didn’t feel he was necessarily quite right for the game with his groin.
‘I don’t think they will be too long, maybe next Saturday. But they are minor knocks.’
A message from the Editor, Mark Waldron
Thank you for reading this story. The dramatic events of 2020 are having a major impact on our advertisers and thus our revenues.
The News is more reliant than ever on you taking out a digital subscription to support our journalism. You can subscribe here for unlimited access to Portsmouth news and information online.
Every subscription helps us continue providing trusted, local journalism and campaign on your behalf for our city.