Wood will leave at the end of March to spend more time in the US and will be replaced by deputy finance director Michael Pratt.
The news comes just three months after chairman Chris Cole announced he would leave at the annual general meeting in September of this year.
Ashtead posted underlying pre-tax profit of £205.1mln for the third quarter to January 31, up 26% on the same period last year.
US President Donald Trump’s tax reforms saw the group’s effective tax rate fall to 31% from 35%, leading to a 52% rise in underlying earnings per share to 32.2p.
Rental revenue rose 24% to £845.5mln with growth across its US, Canada and UK divisions.
The North American construction and industrial rental division, Sunbelt US, delivered a 20% rise in rental revenue as it continued to support clean-up efforts following hurricanes Harvey, Irma and Maria.
The UK equipment hire business A-Plant and the Sunbelt Canada arm achieved rental revenue growth of 15% and 146% respectively.
Currency headwinds expected
Ashtead left its full year guidance unchanged.
“While currency continues to be a headwind, we expect this to be mitigated by the strong underlying performance in North America,” said chief executive Geoff Drabble.
The group sees its capital expenditure for the year reaching the upper end of its guidance at around £1.2bn and anticipates a similar level in fiscal 2018/19.
Capital expenditure in the first nine months of the year came to £859mln and the company spent £315m on bolt-on acquisitions.
Shares fell 3.4% to 1,959 in morning trade.
Full year guidance 'disappointing', says analyst
“Despite an exceptionally strong performance so far this year, guidance for the full year remains unchanged and that’s a bit disappointing," said Nicholas Hyett, equity analyst at Hargreaves Lansdown.
"Management caution seems to be driven by conditions in the foreign exchange markets."
With more than 80% of revenue generated in the US, Ashtead benefitted from a weak pound following the Brexit vote, Hyett pointed out.
"Now it’s the dollar looking wobbly, and that’s creating headwinds since Ashtead’s dollar profits are no longer worth as much in sterling terms," the analyst said.
"Combined with the unexpected departure of CFO Suzanne Wood, it probably explains the share price’s unenthusiastic response to these numbers."