"Finding people that have the right skills is proving to be a challenge" for the industry, said George McFerran, managing director for Asia-Pacific at eFinancial Careers. "There hasn't been an opportunity for a deep talent pool to develop."
The PwC survey indicated hiring experienced wealth managers is bankers' no.1 growth strategy. With the same survey showing bankers expect revenue to grow by 23 percent in 2013 and 21 percent in 2014, the demand for talent can only increase.
The very nature of the business makes it people intensive.
(Read more: Wealth Management Revival as UBS Tops Poll)
"It's a service business and it's not scalable. There are bankers that serve clients and there's only so much a banker can do in a day. They're limited in how many clients they can serve," Pictet's Khanna said.
But he added, Pictet doesn't feel the shortage as much as its rivals, largely because it has been fairly successful at poaching.
In Singapore, Pictet has hired 12 to 13 senior bankers over the past two years, with two hired over the past six months, he said.
"None of the new people that I've hired have jumped," Khanna said. "Pictet is pitching itself in Asia as a senior bankers club. It's a very attractive value proposition," he noted, with the bank seeking employees with at least 20 years' experience.
(Read more: Singapore funds benefit from Asian wealth)
The talent shortage is "absolutely" slowing efforts to grow, said Paul Hodes, head of consumer wealth management for Asia at Citigroup.
"As the business grows, you have to be fully staffed and you have to be fully staffed with the right people," he said, adding the company counters the talent shortage in part by planning its growth over longer periods as well as training employees from the entry level.
(Read more: What's missing in the skills gap? Um...the basics)
"The vast majority of our talent is home grown," he said, noting the bank often recruits people straight out of the university and offers internships. He added that Citigroup puts a great deal of effort into retaining employees.
"It's very difficult to replace people and bring in external people, especially in client-facing positions," he said, noting client relationships often must be developed over a period of decades.
—By CNBC.Com's Leslie Shaffer; Follow her on Twitter