Police Association president Chris Cahill said an argument could be made for urine testing, but blood testing was invasive.
The union was hoping further negotiations with police bosses would lead to a switch to urine testing instead.
"Urine testing is more internationally accepted, and much more appropriate for the workplace environment."
He said he was disappointed by the strong language in the memo, and threat of dismissal.
"There is no legislative requirement for them, so it does come down to an employment and a code of conduct issue."
Cahill said there hadn't been any recorded problems with officers under the influence of drugs or alcohol, before the change was brought in.
Police deputy chief executive of people, Kaye Ryan, said in a statement the directive was formalising what had previously been a voluntary system.
Staff who refused the test would be subject to "an employment process", which she said would be treated on a case by case basis.
"The formalised drug and alcohol testing process brings us into line with many other Police jurisdictions and other safety-critical industries where it is vital that staff in safety-sensitive roles are not impaired by drugs or alcohol and therefore put themselves or others at risk," Ryan said.
"It is also in keeping with the safety principles that apply to the licensed use of firearms by the general public."
Labour police spokesman Stuart Nash said the approach was "very heavy handed".
"It almost seems as if they don't trust the police to use good judgement.
"I wonder what has brought this on.
"I know that every time an officer shoots someone, there's a full investigation.
"I've never heard a suggestion that any officer who's shot someone has been anything other than completely straight."
Nash said random drug testing would be understandable, but this new rule was "most strange".
"If there were suggestions that Armed Offenders Squad members were using drugs, or had turned up to work drunk, or were even misusing legal prescriptions, then yeah we would have reasons to be concerned.
"But there's never been that concern. I'm baffled."