That could sideline the 26-year-old for seven League One matches and an EFL Trophy encounter with West Ham under-21s.
John Marquis will now be handed a recall at Gillingham tomorrow night as the Blues’ only fit conventional striker.
That has left Jackett admitting he would be open to a striking free agent – if the right candidate emerged.
He told The News: ‘Yes, there is that option (for a free agent), we definitely have a space, there is that possibility.
‘If one came up, maybe. We are not imminently doing something, but we do have a space.
‘We’ll see about another striker, we are always looking and our recruitment and scouting won't necessarily stop.
‘Yes, we are constantly looking – but I wouldn’t say there is one close.
‘It would have to be somebody we feel could help us and make a difference.
‘It has got to be the right person fitting in at the right time.’
Pompey will tomorrow submit their 22-man squad to the Football League, with one space available.
Potentially, that can be filled by a free agent, should Jackett so wish.
The Blues also have room in their budget within the confines of the £2.5m salary cap which League One clubs must abide by.
However, Pompey’s boss insists he remains satisfied with his striking options, despite the sudden loss of an in-form Harrison.
He added: ‘There’s John, Ellis and also Marcus. When he has played through the middle has shown a lot of freedom to his game.
‘While Ronan always wants to get among the goals as well.’
A message from the Editor, Mark Waldron
Thank you for reading this story. The News has launched a new subscription offer which gives you unlimited access to all of our Pompey coverage.
You can subscribe here to get the latest news and transfer updates from Fratton Park - and to support our local team of expert Pompey writers.
Every subscription helps us continue providing trusted, local journalism on your behalf for our city.