It is the second time the party’s website has experienced IT difficulties since it was launched in March.
The party claimed the names of those supporting its events were the only details to be hacked and that users could be “confident” the site was secure.
However, the site suffered difficulties on Thursday evening, with the design and graphics of the site failing to load for some users.
In a statement, Kirk Torrance, Alba’s lead candidate in the Highlands and Islands, said “unusual activity” was spotted, but the party was confident the website was “robust”.
He said: “There was some unusual activity at AlbaParty.org yesterday, but we don’t know for sure if we have been the subject of an attack.
"What we do know is our infrastructure was and remains robust to withstand any sort of malicious attack.
"As the underdog in this election, it is clear that the established parties are running scared and so they should be, for Alba is injecting the urgency for independence along with the fresh ideas which Scotland needs to kick start economic recovery and tackle poverty.”
The party said there had been no risk to any data during this second incident and that an investigation was underway to determine the cause of the issues.
It also added the first hack was being investigated by police.