Chief executive Lisa Morgan has left to "pursue other opportunities" while the group's chief operating officer, Terry Scicluna, is also to step down.
The departures – and disappointing trading news – triggered a sell-off, sending shares down as much as 15 per cent at one point. They closed down 11.9 per cent at 89.25p.
Singer analyst Mark Photiades said: "This degree of management change at a time when the business is facing tough conditions is likely to be unsettling."
Morgan has led Game since 2006 but will be replaced by board member and former Ladbrokes boss Chris Bell while a successor is sought.
Markets gave the thumbs-down to a 14.4 per cent fall in like-for-like sales across the group in the 11 weeks to 17 April and a decline of almost 21 per cent in the UK, although Game said this was in line with management expectations.
Seymour Pierce analyst Freddie George called the figures a "major disappointment", and added: "The poor performance in the UK perhaps explains the management departures."
Game reaped the rewards of a booming console market in 2008 with launches such as Nintendo's Wii, but suffered last year in conditions which saw the global console market fall by more than 20 per cent.
The group said its 10 per cent revenues slide outperformed the tough conditions but underlying pre-tax profits were down 27 per cent to 90.4 million in the year to 31 January.