I'd have expected the NHS to have written a better sentence than that! Tell your boss it's terrible. I know it's underfunded, but that's ridiculous.
Inject the contents of One pre-filled syringe by subcuteneous injection once a day.
Inject the contents of one pre-filled syringe subcutaneously once a day.
Your question should begin
'Why is the definite article used ...?'
Student or Learner