She replaces Helen Moon, who has joined the New Connaught Rooms as new business accounts manager.
Allen will focus on corporate accounts, associations and event organisers for new business.
She will also be involved in the Barbican's Olympic sales strategy and oversee its leadership of venue conglomerate the EC Collective.
Allen is MPI UK and Ireland's vice president of partnerships and business opportunities.
Meanwhile, the Barbican's onsite catering supplier, Searcy, has appointed Inga Kamantauskaite as sales and marketing manager.
The Barbican's head of corporate sales, Anthony Hyde, said the venue had "remained positive and forward thinking in our attitude to sales" throughout the recession. "This longer term approach has ensured a strong order book, excellent sales and a full diary," said Hyde. "Samme will be instrumental in our continuing growth, bringing a unique set of skills and experience to the team."