The attacker, and a second raider who punched a member of staff, escaped with cash from The Head Gardener centre in Salford.
The robbery on 8 August was described by local police as a "terrifying raid".
A representative for the centre said that at around 4.30pm two men entered the garden centre. "One man, armed with a machete, approached the manager and demanded cash.
"A second offender went upstairs and punched a member of staff in the face before ordering him and another member of staff downstairs. The man with the machete grabbed the arm of one of the employees and threatened to chop it off. The men then escaped with an amount of cash in a Renault Laguna," added the representative.
Detective inspector Caroline Walker added: "The offenders were extremely dangerous and made shocking threats but thankfully no one was seriously hurt."
Police are appealing for witnesses in Barton Business Park to contact them. Both thieves are white and in their 20s or early 30s.