Note 4 - Warrants (Details Textual) - USD ($)	3 Months Ended
Mar. 31, 2022	Mar. 31, 2021	Dec. 31, 2021	Aug. 31, 2021	Apr. 30, 2021
Share-Based Payment Arrangement, Expense	$ 527,000	$ 405,000
Equity Classified Warrants [Member]
Class of Warrant or Right, Number of Securities Called by Warrants or Rights (in shares)	396,502		396,502	250,000	71,500
Warrants and Rights Outstanding, Term (Year)				10 years	5 years
Class of Warrant or Right, Exercise Price of Warrants or Rights (in dollars per share)				$ 3.08	$ 3.63
Class of Warrant or Right, Vested and Exercisable (in shares)	190,135		186,560
Share-Based Payment Arrangement, Expense	$ 83,000	$ 0
Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount	$ 465,000

Number of warrants or rights vested and exercisable.

No definition available.

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Namespace Prefix:	mbrx_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of cost not yet recognized for nonvested award under share-based payment arrangement.

+ References

No definition available.

+ Details

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Namespace Prefix:	mbrx_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (h)(1)(i)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Exercise price per share or per unit of warrants or rights outstanding.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 3
-URI https://asc.fasb.org/extlink&oid=126973232&loc=d3e21475-112644

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of securities into which the class of warrant or right may be converted. For example, but not limited to, 500,000 warrants may be converted into 1,000,000 shares.

+ References

+ Details

Name:	us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Period between issuance and expiration of outstanding warrant and right embodying unconditional obligation requiring redemption by transferring asset at specified or determinable date or upon event certain to occur, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-URI https://asc.fasb.org/extlink&oid=126976982&loc=d3e19207-110258

+ Details

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Namespace Prefix:	us-gaap_
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Balance Type:	na
Period Type:	instant

- Details

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Namespace Prefix:
Data Type:	na
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