She smiled and shook hands with a voter as she left.
The election is to fill 90 seats in the Northern Ireland Assembly, after a previous decision to reduce the number of lawmakers from 108 in a cost-cutting measure.
Polling stations opened at 7am and will close at 10pm.
Former Conservative defence minister Sir Gerald Howarth said the United Kingdom government should not back down on insisting on the investigations. Sinn Fein brought down the assembly in January over the issue.
Nearly 230 candidates are running.
But in a province where almost 56 per cent of the population voted Remain in the European Union referendum, last week's Northern Irish election - and the big gains for republicans and nationalists - may have consequences for Brexit even if unionists do not yet recognise it.
Sinn Fein, the former political wing of the Irish Republican Army, has for weeks insisted that it will not support the nomination of Foster as first minister while months of investigations get underway into the abuse of the heating subsidy she established as a minister.
The whole point of power-sharing - the central goal of Northern Ireland's 1998 peace accord - is to promote compromise between two evenly balanced blocs. Vote counting is expected to start on Friday with final results due over the weekend.More news: Meet Young Jack Sparrow In The New Pirates Of The Caribbean Trailer
The largest party, the DUP, is running 38 - six fewer than past year.
The DUP and Sinn Fein will have three weeks to form a new power-sharing government to avoid devolved power returning to Westminster for the first time in a decade.
"But this is a possible solution that I think Sinn Fein would go for and it would enable Arlene to regain lost ground".
Reflecting on the results of the Stormont poll, which saw Sinn Fein make huge gains across Northern Ireland, Mr Morrison commented: "2017 will be remembered as a terrible year for unionism".
The reimposition of direct rule from London is on the cards if the post-election talks fail. The remaining 11 seats are held by non-sectarian parties: eight for the liberal Alliance, two Greens, and one Trotskyist.
Their government collapsed in January after Sinn Fein withdrew support over Foster's handling of a controversial energy scheme.
As the results of the NI Assembly election filter through, it is becoming clear that the election has been a success for Sinn Fein, who have taken 27.9% of the first preference vote - 3.9% up from a year ago, and just behind the DUP on 28.1%.
"Sinn Féin won't back down on this one".