A yellow "be aware" warning has been issued for late Thursday into Friday for the Western and Northern Isles, Highlands and Argyll.
The warning also applies to parts of Moray and Aberdeenshire.
Earlier this year the Met Office asked the public for suggestions for names for storms.
Storm Abigail could bring gusts of 60 to 70mph, potentially rising to speeds of up to 80mph in exposed areas.
The warning is in place from 18:00 on Thursday until 14:00 on Friday.
In its warning, the Met Office said: "The public should be aware of the risk of disruption to transport. In addition, large waves may give rise to local over-topping along some coasts.
"A vigorous depression is expected to pass just to the northwest of Scotland on Thursday night bringing a swathe of very strong winds on its eastern and southern flanks.
"There remains some uncertainty regarding the exact extent and timing of strongest winds and the extent of impacts and this warning will be kept under review."
Sea swell charts produced by South Devon-based surfing website Magicseaweed.com suggest swell reaching heights of 10-11.5m (36-38ft) on Friday.
Meteorologist Dr Eddy Graham, who lectures at Lews Castle College UHI in Stornoway in Lewis, said people should stay indoors if the weather deteriorates.
He said: "The Met Office have issued the first high wind warning of the season for this Thursday and Friday for most of northern and western Scotland.
"Winds are expected to reach over 70mph, possibly touching 80mph in the strongest gusts. Winds of these speeds are dangerous when outdoors - stay safely indoors when conditions deteriorate."

The 2016 Rio Olympics GB Sevens silver medallist appeared to use a gesture and swear at referee Greg Garner.
Scarlets have condemned Davies' "abusive language or actions".
In a statement, the player said: "I would like to apologise to my team-mates, the fans, the Scarlets, my family and the rugby community."
In the 28th minute at Stade Felix Mayol, Garner called over Davies and Scarlets captain Ken Owens and told Davies: "If you use that language again on the pitch, I'll send you off."
Davies said he had apologised to English official Garner during and after the game.
He added: "During the heat of battle I lost my composure and said and did things I deeply regret.
"I apologised to referee Mr Garner both during and after the game but would like to reiterate my sincerest apologies publically."
A Scarlets spokesperson said: "The Scarlets hold the unique values of rugby union in the highest regard.
"Our players are all aware of their responsibility as role models and custodians of those values.
"We unreservedly condemn any foul or abusive language or actions like those displayed by James Davies on Sunday."
Davies could now face disciplinary action that could affect his chances of facing Toulon in their rematch at Parc y Scarlets, Llanelli on Sunday.
Scarlets say they will comply fully with "disciplinary procedures" and conduct an internal investigation into the incident.
Storm Abigail, the first storm to be officially named by the Met Office, is set to bring winds of up to 80mph to parts of Scotland later this week.
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Scarlets flanker James Davies has apologised for his "unforgiveable actions" in their European Champions Cup defeat at Toulon on Sunday.