At least two supporters entered the playing area during the second half in which Burnley scored three times to win 3-0 and leave West Ham in relegation danger from the Premier League.
One of the fans, a 61-year-old businessman, took a corner flag and planted it in the centre circle to protest the club's move from Upton Park Stadium.
West Ham co-owners David Gold and David Sullivan were verbally abused and had coins thrown at them in the directors' box as fans congregated below.
The club, which moved into the Olympic 2012 stadium, now known as the London Stadium, at the beginning of last season as lead tenants, have held emergency meetings with stakeholders.
"West Ham United are committed to taking decisive and positive action with the primary focus of ensuring London Stadium is a safe, comfortable and secure environment for supporters attending future matches," a statement said.
"Following the incidents which marred the second half of the Premier League fixture with Burnley, the Club is conducting a full and thorough investigation, and has attended a series of emergency meetings with London Stadium stakeholders.
"The Club is working in close conjunction with the Metropolitan Police to identify those individuals, who entered the pitch during the second half, and with stadium operator LS185, using London Stadium's high-quality CCTV footage, to identify those who threw missiles, both of which are specific offences under the Football (Offences) Act 1991."
"Any individual found guilty will be banned from attending any West Ham United fixture, home and away, for life and the Club will request the courts serve a banning order to prevent these individuals attending any football matches in future."
While West Ham announced a 43.5 million pounds ($60.73 million) profit in the year ending May 2017 and record turnover of 183.3 million pounds -- coinciding with the move away from Upton Park -- results on the pitch have continued to decline.
West Ham are two places, and three points, above the relegation zone with eight matches to play, including several against clubs in the top six.
That and a perceived loss of identity following the move to the London Stadium, has fuelled fans' unrest but West Ham says it has a "zero-tolerance" policy towards bad behaviour.
Another meeting with various stadium stakeholders and the Metropolitan Police is planned for Thursday.
"The Club will make clear that its primary concern is for the safety and comfort of its supporters on matchdays and, to that end, will lead discussions centred on the safety management plans put in place and the policing and stewarding for future fixtures at London Stadium," a statement said.
($1 = 0.7163 pounds) (Reporting by Martyn Herman; Editing by John O'Brien)