Nope. 555 has drive capability of over 100mA. More than enough to drive a small relay directly. Just make sure you have a spike suppression diode in circuit.
Good tip: measure voltage between the output pin and gnd or Vcc in both states and then have a think.
Plus when you're not an idiot like I was, a MOSFET is cheaper.
I sometimes overestimate the ability of the average electronics hobbyist to properly understand a datasheet.