It is highly unlikely she was literally a virgin queen - I assume you mean someone who never had sexual intercourse. She was pursued by Thomas Seymour at age 14, who was at the time uncle to King Edward VI. Elizabeth lived in his house with the dowager queen Catherine Parr, and he engaged in a lot of inappropriate sexual play with her. Whether or not they actually had sex is up for debate.
Later in life though, she apparently fell in love with a longtime friend, Robert Dudley. This affection lasted for a long time, even after Dudley remarried (his first wife died). I can't find any definitive information on if they consummated their relationship or not, but he is the most likely candidate for it. I have read that Elizabeth was thought to be cold towards sexual relationships because of Thomas Seymour's unwelcome sexual advances when she was 14.
Other candidates included the French Dukes of Anjou, Henry and Francis (the latter of which she considered marrying).
To give you a short answer, she was almost certainly not literally a virgin - but she may as well have been.
My source is Weir's Life of Elizabeth I, much less for its analysis than for simply collecting primary sources and general knowledge.
As you could imagine, her virginity is quite contested. So, if she was a virgin, it might be, as Ben Jonson wrote, due to a medical problem, instead of something-something-merry-old-England.
That she had a membrane on her, which made her incapable of man, though for her delight she tried many.
If she did have sex, there's two significant contenders. First is Thomas Seymour. The big source is Elizabeth's governess who wrote to Mrs. Seymour about inappropriate behavior on Thomas' part. Catherine dismissed it. After Catherine's death there's some further mumblings that he was still pursuing Elizabeth and she was cold to him. But there is nothing that intends actual sexual behavior.
The second possibility is Robert Dudley, who literally lived next door, whose wife mysteriously died, and who hung around court, single, for twenty years. Again, though, there is no evidence of any kind, just speculation.
The popular imagination often contends that Seymour raped her and then Dudley was either her loyal minion or her lover. But there's nothing definitive.
Will and Ariel Durant touch on this in "The Age of Reason Begins," part seven of their "Story of Civilization." On her virginity:
This condition, of course, is a recondite detail on which historians must not pretend to certainty... Cecil, watching Elizabeth's long flirtation with Leicester, had some passing doubts, but two Spanish ambassadors, not loath to dishonor the Queen, concluded her honor. The gossip of the court, as reported by Ben Jonson to Drummond of Hawthornden, held that "she had a membrane on her which made her incapable of man, though for her delight she tried many. ... A French surgeon undertook to cut it, yet fear stayed her." "The people," wrote Camden in his Annales (1615), "cursed Huic, the Queen's physician, as having dissuaded the Queen from marrying on account of some impediment and defect in her." Yet Parliament, repeatedly begging her to marry, assumed her capacity to bear. Something went wrong, in this regard, with most of Tudor royalty: probably the misfortunes of Catherine of Aragon in childbirth were due to Henry VIII's syphilis; his son Edward died in youth of some ill-described disease; his daughter Mary tried fervently to have a child, only to mistake dropsy for pregnancy; and Elizabeth, though she flirted as long as she could walk, never ventured on marriage. "I have always shrunk from it," she said, and as early as 1558 she declared her intention to remain a virgin. In 1566 she promised Parliament, "I will marry as soon as I can conveniently ... and I hope to have children." But in that same year, when Cecil told her that Mary Stuart had born a son, Elizabeth almost wept, and said, "The Queen of Scots is the mother of a fair son, and I am but a barren stock." There for a moment she revealed her lasting grief—that she could not fulfill her womanhood.