National Australia Bank (NAB) said it had made contingency plans should the referendum next month turn out in favour of a split from the UK.
The warning on independence comes after Royal Bank of Scotland earlier this month reiterated its stance that a Yes vote could have a "material adverse effect" on it.
NAB chief executive Andrew Thorburn referred to the Scottish referendum as one of a number of challenges facing NAB's UK operations - in addition to charges for past conduct.
He said: "A vote in favour of independence may give rise to significant additional costs and risks for Clydesdale Bank. We continue to closely monitor the situation and have appropriate contingency planning in place."
Meanwhile, Clydesdale and Yorkshire Banks saw provisions for dealing with past mis-selling scandals swell to more than £800 million as its boss admitted the way it had dealt with payment protection insurance (PPI) claims had "not been consistent".
Changes to this process are likely to result in higher pay-outs and revisions to past compensation, NAB said.
Mr Thorburn added that the group would need to take further provisions for the full year for PPI mis-selling compensation as well as for misconduct over interest rate hedging products - complex financial products that were sold to small firms.
NAB reported cash earnings up 7% to 1.6 billion Australian dollars (£891 million) for the third quarter to the end of June as bad debt charges in Australia and the UK fell. Meanwhile, last month it disposed of £625 million of UK commercial property loans.
The group said it expected to make an additional £75 million provision at the end of the financial year because of "increased costs of administering the PPI remediation programme". This takes the total put aside for PPI redress to £461 million.
Provision for interest rate hedging products will be nearly doubled, with an additional sum of at least £170 million set aside taking the total to £350 million.
It will take the total running cost for both scandals to £811 million.
NAB said on top of this there were also likely to be "significant additional provisions" for PPI as a new complaints handling process is introduced.
This was "likely to lead to increased payments both for new complaints and in revisiting closed complaints", it said.
Mr Thorburn said: "In line with the industry, we continue to deal with legacy issues.
"The way we've handled historic PPI complaints has not been consistent, and we are committed to putting this right.
"We have already introduced a new PPI complaint handing process, and we will also apply this new process to a systematic and proactive review of all past PPI complaints.
Labour shadow business minister Ian Murray said: "Anyone who sees these latest comments will wonder if all of this risk, all of this uncertainty, and all of these unanswered questions are worth it.
"The risks posed by separation has seen some of our biggest employers make contingency plans. It is really worrying that jobs in Scotland are at risk.
"Despite this, Alex Salmond refuses to name his own Plan B on currency."
Mr Murray, the MP for Edinburgh South, said the First Minister "cannot continue to duck this question, it is simply too important for the people of Scotland".
He continued: "People will begin casting their vote by post next week, they deserve answers now. Alex Salmond cannot ask us to risk everything on their crossed fingers.
"We do not have to take that risk. We can have the best of both worlds for Scotland - a strong Scottish Parliament, with more powers guaranteed, backed up by the strength, security and stability of the UK by saying No Thanks to separation on September 18."
A Scottish Government spokeswoman said: "The Scottish Government welcomes the action Clydesdale Bank is taking to compensate customers for previous poor practice.
"Scotland is one of the wealthiest countries in the world, more prosperous per head than France, Japan and the UK itself, but we need the powers of independence to make the most of our huge resources.
"Following a vote for independence, Scotland would continue to use Sterling. As set out in Scotland's Future, there would be formal arrangements that would ensure both currency and regulation would be harmonised in the best interests of customers and businesses on both sides of the border and Scotland would remain a member of the EU.
"An independent Scotland would be a hugely attractive place to do business and to invest in. We welcome the commitment from many businesses who are fully committed to Scotland, whatever the nation's constitutional future."